diff --git a/dvc/fs/base.py b/dvc/fs/base.py
index e7c757bc5..99a06e929 100644
--- a/dvc/fs/base.py
+++ b/dvc/fs/base.py
@@ -187,7 +187,7 @@ class BaseFileSystem:
     def remove(self, path_info):
         raise RemoteActionNotImplemented("remove", self.scheme)
 
-    def makedirs(self, path_info):
+    def makedirs(self, path_info, **kwargs):
         """Optional: Implement only if the remote needs to create
         directories before copying/linking/moving data
         """
diff --git a/dvc/fs/fsspec_wrapper.py b/dvc/fs/fsspec_wrapper.py
index 53d52889a..9b4a67de7 100644
--- a/dvc/fs/fsspec_wrapper.py
+++ b/dvc/fs/fsspec_wrapper.py
@@ -22,21 +22,11 @@ class FSSpecWrapper(BaseFileSystem):
     def fs(self):
         raise NotImplementedError
 
-    @lru_cache(512)
     def _with_bucket(self, path):
-        if isinstance(path, self.PATH_CLS):
-            return f"{path.bucket}/{path.path}"
-        return path
+        return str(path)
 
     def _strip_bucket(self, entry):
-        try:
-            bucket, path = entry.split("/", 1)
-        except ValueError:
-            # If there is no path attached, only returns
-            # the bucket (top-level).
-            bucket, path = entry, None
-
-        return path or bucket
+        return entry
 
     def _strip_buckets(self, entries, detail=False):
         for entry in entries:
@@ -86,6 +76,7 @@ class FSSpecWrapper(BaseFileSystem):
         return self.fs.open(self._with_bucket(path_info), mode=mode)
 
     def copy(self, from_info, to_info):
+        self.makedirs(to_info.parent)
         self.fs.copy(self._with_bucket(from_info), self._with_bucket(to_info))
 
     def exists(self, path_info) -> bool:
@@ -118,18 +109,25 @@ class FSSpecWrapper(BaseFileSystem):
         info["name"] = self._strip_bucket(info["name"])
         return info
 
+    def makedirs(self, path_info, **kwargs):
+        self.fs.makedirs(
+            self._with_bucket(path_info), exist_ok=kwargs.pop("exist_ok", True)
+        )
+
     def _upload_fobj(self, fobj, to_info, size=None):
+        self.makedirs(to_info.parent)
         with self.open(to_info, "wb") as fdest:
             shutil.copyfileobj(fobj, fdest, length=fdest.blocksize)
 
     def _upload(
         self, from_file, to_info, name=None, no_progress_bar=False, **kwargs
     ):
+        self.makedirs(to_info.parent)
         size = os.path.getsize(from_file)
         with open(from_file, "rb") as fobj:
             self.upload_fobj(
                 fobj,
-                self._with_bucket(to_info),
+                to_info,
                 size=size,
                 desc=name,
                 no_progress_bar=no_progress_bar,
@@ -158,6 +156,29 @@ class FSSpecWrapper(BaseFileSystem):
 class ObjectFSWrapper(FSSpecWrapper):
     TRAVERSE_PREFIX_LEN = 3
 
+    @lru_cache(512)
+    def _with_bucket(self, path):
+        if isinstance(path, self.PATH_CLS):
+            return f"{path.bucket}/{path.path}"
+        return path
+
+    def _strip_bucket(self, entry):
+        try:
+            bucket, path = entry.split("/", 1)
+        except ValueError:
+            # If there is no path attached, only returns
+            # the bucket (top-level).
+            bucket, path = entry, None
+        return path or bucket
+
+    def makedirs(self, path_info, **kwargs):
+        # For object storages make this method a no-op. The original
+        # fs.makedirs() method will only check if the bucket exists
+        # and create if it doesn't though we don't want to support
+        # that behavior, and the check will cost some time so we'll
+        # simply ignore all mkdir()/makedirs() calls.
+        return None
+
     def _isdir(self, path_info):
         # Directory in object storages are interpreted differently
         # among different fsspec providers, so this logic is a temporary
diff --git a/dvc/fs/hdfs.py b/dvc/fs/hdfs.py
index b2893d255..3e906340a 100644
--- a/dvc/fs/hdfs.py
+++ b/dvc/fs/hdfs.py
@@ -183,7 +183,7 @@ class HDFSFileSystem(BaseFileSystem):
                 else:
                     hdfs.delete_file(path_info.path)
 
-    def makedirs(self, path_info):
+    def makedirs(self, path_info, **kwargs):
         with self.hdfs(path_info) as hdfs:
             # NOTE: fs.create_dir creates parents by default
             hdfs.create_dir(path_info.path)
diff --git a/dvc/fs/local.py b/dvc/fs/local.py
index 147cb06fa..4c02b54d9 100644
--- a/dvc/fs/local.py
+++ b/dvc/fs/local.py
@@ -79,8 +79,8 @@ class LocalFileSystem(BaseFileSystem):
                 raise NotImplementedError
         remove(path_info)
 
-    def makedirs(self, path_info):
-        makedirs(path_info, exist_ok=True)
+    def makedirs(self, path_info, **kwargs):
+        makedirs(path_info, exist_ok=kwargs.pop("exist_ok", True))
 
     def isexec(self, path_info):
         mode = self.stat(path_info).st_mode
diff --git a/dvc/fs/ssh/__init__.py b/dvc/fs/ssh/__init__.py
index 496e25043..2fca225c2 100644
--- a/dvc/fs/ssh/__init__.py
+++ b/dvc/fs/ssh/__init__.py
@@ -173,7 +173,7 @@ class SSHFileSystem(BaseFileSystem):  # pylint:disable=abstract-method
         with self.ssh() as ssh:
             ssh.remove(path_info.path)
 
-    def makedirs(self, path_info):
+    def makedirs(self, path_info, **kwargs):
         with self.ssh() as ssh:
             ssh.makedirs(path_info.path)
 
diff --git a/dvc/fs/webdav.py b/dvc/fs/webdav.py
index d7e5e11a7..7f9d6788a 100644
--- a/dvc/fs/webdav.py
+++ b/dvc/fs/webdav.py
@@ -81,10 +81,6 @@ class WebDAVFileSystem(FSSpecWrapper):  # pylint:disable=abstract-method
             fobj, rpath, overwrite=True, size=size
         )
 
-    def makedirs(self, path_info):
-        path = self.translate_path_info(path_info)
-        return self.fs.makedirs(path, exist_ok=True)
-
     @lru_cache(512)
     def translate_path_info(self, path):
         if isinstance(path, self.PATH_CLS):
@@ -93,9 +89,6 @@ class WebDAVFileSystem(FSSpecWrapper):  # pylint:disable=abstract-method
 
     _with_bucket = translate_path_info
 
-    def _strip_bucket(self, entry):
-        return entry
-
 
 class WebDAVSFileSystem(WebDAVFileSystem):  # pylint:disable=abstract-method
     scheme = Schemes.WEBDAVS
diff --git a/tests/func/test_fs.py b/tests/func/test_fs.py
index bbfe95bf3..96154f9d7 100644
--- a/tests/func/test_fs.py
+++ b/tests/func/test_fs.py
@@ -1,3 +1,4 @@
+import io
 import os
 from operator import itemgetter
 from os.path import join
@@ -324,7 +325,7 @@ def test_fs_ls(dvc, cloud):
         pytest.lazy_fixture("gdrive"),
     ],
 )
-def test_fs_find_recursive(dvc, cloud):
+def test_fs_find(dvc, cloud):
     cloud.gen({"data": {"foo": "foo", "bar": {"baz": "baz"}, "quux": "quux"}})
     cls, config, path_info = get_cloud_fs(dvc, **cloud.config)
     fs = cls(**config)
@@ -382,3 +383,28 @@ def test_fs_fsspec_path_management(dvc, cloud):
     data_details = fs.info(data)
     assert data_details["name"].rstrip("/") == data.path
     assert data_details["type"] == "directory"
+
+
+@pytest.mark.needs_internet
+@pytest.mark.parametrize(
+    "cloud",
+    [
+        pytest.lazy_fixture("azure"),
+        pytest.lazy_fixture("gs"),
+        pytest.lazy_fixture("s3"),
+        pytest.lazy_fixture("webdav"),
+    ],
+)
+def test_fs_makedirs_on_upload_and_copy(dvc, cloud):
+    cls, config, _ = get_cloud_fs(dvc, **cloud.config)
+    fs = cls(**config)
+
+    with io.BytesIO(b"foo") as stream:
+        fs.upload_fobj(stream, cloud / "dir" / "foo")
+
+    assert fs.isdir(cloud / "dir")
+    assert fs.exists(cloud / "dir" / "foo")
+
+    fs.copy(cloud / "dir" / "foo", cloud / "dir2" / "foo")
+    assert fs.isdir(cloud / "dir2")
+    assert fs.exists(cloud / "dir2" / "foo")