diff --git a/dvc/fs/base.py b/dvc/fs/base.py
index 9ffbe69a4..891207bdb 100644
--- a/dvc/fs/base.py
+++ b/dvc/fs/base.py
@@ -283,6 +283,9 @@ class BaseFileSystem:
         self, from_info, to_info, name, no_progress_bar, jobs, **kwargs,
     ):
         from_infos = list(self.walk_files(from_info, **kwargs))
+        if not from_infos:
+            makedirs(to_info, exist_ok=True)
+            return None
         to_infos = (
             to_info / info.relative_to(from_info) for info in from_infos
         )
diff --git a/dvc/fs/fsspec_wrapper.py b/dvc/fs/fsspec_wrapper.py
index b4c730ce7..1550d69ec 100644
--- a/dvc/fs/fsspec_wrapper.py
+++ b/dvc/fs/fsspec_wrapper.py
@@ -1,5 +1,6 @@
 import os
 import shutil
+from functools import lru_cache
 
 from dvc.progress import Tqdm
 
@@ -11,6 +12,7 @@ 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}"
@@ -37,10 +39,32 @@ class FSSpecWrapper(BaseFileSystem):
         return entry
 
     def isdir(self, path_info):
-        return self.fs.isdir(self._with_bucket(path_info))
+        if not self.exists(path_info):
+            return False
+
+        # Directory in object storages are interpreted differently
+        # among different fsspec providers, so this logic is a temporary
+        # measure for us to adapt as of now. It checks whether it is a
+        # directory (as in a prefix with contents) or whether it is an empty
+        # file where it's name ends with a forward slash
+        entry = self.info(path_info)
+        return entry["type"] == "directory" or (
+            entry["size"] == 0
+            and entry["type"] == "file"
+            and entry["name"].endswith("/")
+        )
 
     def isfile(self, path_info):
-        return self.fs.isfile(self._with_bucket(path_info))
+        if not self.exists(path_info):
+            return False
+
+        return not self.isdir(path_info)
+
+    def is_empty(self, path_info):
+        entry = self.info(path_info)
+        if entry["type"] == "directory":
+            return not self.fs.ls(self._with_bucket(path_info))
+        return entry["size"] == 0
 
     def open(
         self, path_info, mode="r", **kwargs
@@ -56,6 +80,9 @@ class FSSpecWrapper(BaseFileSystem):
     def ls(
         self, path_info, detail=False, recursive=False
     ):  # pylint: disable=arguments-differ
+        if self.isdir(path_info) and self.is_empty(path_info):
+            return None
+
         path = self._with_bucket(path_info)
         if recursive:
             for root, _, files in self.fs.walk(path, detail=detail):
diff --git a/tests/func/test_import_url.py b/tests/func/test_import_url.py
index 738b05521..28d03ab23 100644
--- a/tests/func/test_import_url.py
+++ b/tests/func/test_import_url.py
@@ -353,3 +353,42 @@ def test_import_url_to_remote_absolute(
 def test_import_url_to_remote_invalid_combinations(dvc):
     with pytest.raises(InvalidArgumentError, match="--no-exec"):
         dvc.imp_url("s3://bucket/foo", no_exec=True, to_remote=True)
+
+
+empty_xfail = pytest.mark.xfail(
+    reason="https://github.com/iterative/dvc/issues/5521"
+)
+
+
+@pytest.mark.parametrize(
+    "workspace",
+    [
+        pytest.lazy_fixture("s3"),
+        pytest.lazy_fixture("hdfs"),
+        pytest.param(pytest.lazy_fixture("gs"), marks=empty_xfail),
+        pytest.param(pytest.lazy_fixture("azure"), marks=empty_xfail),
+        pytest.param(
+            pytest.lazy_fixture("ssh"),
+            marks=pytest.mark.skipif(
+                os.name == "nt", reason="disabled on windows"
+            ),
+        ),
+    ],
+    indirect=True,
+)
+def test_import_url_empty_directory(tmp_dir, dvc, workspace):
+    # prefix based storage services (e.g s3) doesn't have the real concept
+    # of directories. So instead we create an empty file that ends with a
+    # trailing slash in order to actually support this operation
+    if workspace.IS_OBJECT_STORAGE:
+        contents = ""
+    else:
+        contents = {}
+
+    workspace.gen({"empty_dir/": contents})
+
+    dvc.imp_url("remote://workspace/empty_dir/")
+
+    empty_dir = tmp_dir / "empty_dir"
+    assert empty_dir.is_dir()
+    assert tuple(empty_dir.iterdir()) == ()
diff --git a/tests/remotes/azure.py b/tests/remotes/azure.py
index 14306a472..c288302a5 100644
--- a/tests/remotes/azure.py
+++ b/tests/remotes/azure.py
@@ -22,6 +22,7 @@ TEST_AZURE_CONNECTION_STRING = (
 
 class Azure(Base, CloudURLInfo):
 
+    IS_OBJECT_STORAGE = True
     CONNECTION_STRING = None
 
     @cached_property
diff --git a/tests/remotes/base.py b/tests/remotes/base.py
index 704503f3f..ea5fb79bb 100644
--- a/tests/remotes/base.py
+++ b/tests/remotes/base.py
@@ -7,6 +7,9 @@ from dvc.path_info import URLInfo
 
 
 class Base(URLInfo):
+
+    IS_OBJECT_STORAGE = False
+
     def is_file(self):
         raise NotImplementedError
 
diff --git a/tests/remotes/gs.py b/tests/remotes/gs.py
index 0099ccc84..0418fc94e 100644
--- a/tests/remotes/gs.py
+++ b/tests/remotes/gs.py
@@ -23,6 +23,9 @@ os.environ["GOOGLE_APPLICATION_CREDENTIALS"] = TEST_GCP_CREDS_FILE
 
 
 class GCP(Base, CloudURLInfo):
+
+    IS_OBJECT_STORAGE = True
+
     @staticmethod
     def should_test():
         do_test = env2bool("DVC_TEST_GCP", undefined=None)
diff --git a/tests/remotes/oss.py b/tests/remotes/oss.py
index 43fbb4a77..e84f3948c 100644
--- a/tests/remotes/oss.py
+++ b/tests/remotes/oss.py
@@ -16,6 +16,9 @@ EMULATOR_OSS_ACCESS_KEY_SECRET = "AccessKeySecret"
 
 
 class OSS(Base, CloudURLInfo):
+
+    IS_OBJECT_STORAGE = True
+
     @staticmethod
     def get_url():
         return f"oss://{TEST_OSS_REPO_BUCKET}/{uuid.uuid4()}"
diff --git a/tests/remotes/s3.py b/tests/remotes/s3.py
index 22f8c9a3d..b0517c221 100644
--- a/tests/remotes/s3.py
+++ b/tests/remotes/s3.py
@@ -15,6 +15,9 @@ TEST_AWS_REPO_BUCKET = os.environ.get("DVC_TEST_AWS_REPO_BUCKET", "dvc-temp")
 
 
 class S3(Base, CloudURLInfo):
+
+    IS_OBJECT_STORAGE = True
+
     @staticmethod
     def should_test():
         do_test = env2bool("DVC_TEST_AWS", undefined=None)