diff --git a/spacy/cli/_util.py b/spacy/cli/_util.py
index ed1e840a5..127bba55a 100644
--- a/spacy/cli/_util.py
+++ b/spacy/cli/_util.py
@@ -397,7 +397,11 @@ def git_checkout(
         run_command(cmd, capture=True)
         # We need Path(name) to make sure we also support subdirectories
         try:
-            shutil.copytree(str(tmp_dir / Path(subpath)), str(dest))
+            source_path = tmp_dir / Path(subpath)
+            if not is_subpath_of(tmp_dir, source_path):
+                err = f"'{subpath}' is a path outside of the cloned repository."
+                msg.fail(err, repo, exits=1)
+            shutil.copytree(str(source_path), str(dest))
         except FileNotFoundError:
             err = f"Can't clone {subpath}. Make sure the directory exists in the repo (branch '{branch}')"
             msg.fail(err, repo, exits=1)
@@ -445,8 +449,14 @@ def git_sparse_checkout(repo, subpath, dest, branch):
         # And finally, we can checkout our subpath
         cmd = f"git -C {tmp_dir} checkout {branch} {subpath}"
         run_command(cmd, capture=True)
-        # We need Path(name) to make sure we also support subdirectories
-        shutil.move(str(tmp_dir / Path(subpath)), str(dest))
+
+        # Get a subdirectory of the cloned path, if appropriate
+        source_path = tmp_dir / Path(subpath)
+        if not is_subpath_of(tmp_dir, source_path):
+            err = f"'{subpath}' is a path outside of the cloned repository."
+            msg.fail(err, repo, exits=1)
+
+        shutil.move(str(source_path), str(dest))
 
 
 def get_git_version(
@@ -477,6 +487,19 @@ def _http_to_git(repo: str) -> str:
     return repo
 
 
+def is_subpath_of(parent, child):
+    """
+    Check whether `child` is a path contained within `parent`.
+    """
+    # Based on https://stackoverflow.com/a/37095733 .
+
+    # In Python 3.9, the `Path.is_relative_to()` method will supplant this, so
+    # we can stop using crusty old os.path functions.
+    parent_realpath = os.path.realpath(parent)
+    child_realpath = os.path.realpath(child)
+    return os.path.commonpath([parent_realpath, child_realpath]) == parent_realpath
+
+
 def string_to_list(value: str, intify: bool = False) -> Union[List[str], List[int]]:
     """Parse a comma-separated string to a list and account for various
     formatting options. Mostly used to handle CLI arguments that take a list of
diff --git a/spacy/cli/project/assets.py b/spacy/cli/project/assets.py
index b49e18608..efa4d637a 100644
--- a/spacy/cli/project/assets.py
+++ b/spacy/cli/project/assets.py
@@ -59,6 +59,10 @@ def project_assets(project_dir: Path, *, sparse_checkout: bool = False) -> None:
                         shutil.rmtree(dest)
                     else:
                         dest.unlink()
+            if "repo" not in asset["git"] or asset["git"]["repo"] is None:
+                msg.fail("A git asset must include 'repo', the repository address.", exits=1)
+            if "path" not in asset["git"] or asset["git"]["path"] is None:
+                msg.fail("A git asset must include 'path' - use \"\" to get the entire repository.", exits=1)
             git_checkout(
                 asset["git"]["repo"],
                 asset["git"]["path"],
diff --git a/spacy/tests/test_cli.py b/spacy/tests/test_cli.py
index e84159b64..ae4cec17d 100644
--- a/spacy/tests/test_cli.py
+++ b/spacy/tests/test_cli.py
@@ -9,6 +9,7 @@ from spacy.cli import info
 from spacy.cli.init_config import init_config, RECOMMENDATIONS
 from spacy.cli._util import validate_project_commands, parse_config_overrides
 from spacy.cli._util import load_project_config, substitute_project_variables
+from spacy.cli._util import is_subpath_of
 from spacy.cli._util import string_to_list
 from spacy import about
 from spacy.util import get_minor_version
@@ -542,3 +543,18 @@ def test_get_third_party_dependencies_runs():
     # Test with component factory based on Cython module
     nlp.add_pipe("tagger")
     assert get_third_party_dependencies(nlp.config) == []
+
+
+@pytest.mark.parametrize(
+    "parent,child,expected",
+    [
+        ("/tmp", "/tmp", True),
+        ("/tmp", "/", False),
+        ("/tmp", "/tmp/subdir", True),
+        ("/tmp", "/tmpdir", False),
+        ("/tmp", "/tmp/subdir/..", True),
+        ("/tmp", "/tmp/..", False)
+    ],
+)
+def test_is_subpath_of(parent, child, expected):
+    assert is_subpath_of(parent, child) == expected
diff --git a/website/docs/usage/projects.md b/website/docs/usage/projects.md
index a646989a5..6f6cef7c8 100644
--- a/website/docs/usage/projects.md
+++ b/website/docs/usage/projects.md
@@ -291,7 +291,7 @@ files you need and not the whole repo.
 | Name          | Description                                                                                                                                                                                          |
 | ------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
 | `dest`        | The destination path to save the downloaded asset to (relative to the project directory), including the file name.                                                                                   |
-| `git`         | `repo`: The URL of the repo to download from.<br />`path`: Path of the file or directory to download, relative to the repo root.<br />`branch`: The branch to download from. Defaults to `"master"`. |
+| `git`         | `repo`: The URL of the repo to download from.<br />`path`: Path of the file or directory to download, relative to the repo root. "" specifies the root directory.<br />`branch`: The branch to download from. Defaults to `"master"`. |
 | `checksum`    | Optional checksum of the file. If provided, it will be used to verify that the file matches and downloads will be skipped if a local file with the same checksum already exists.                     |
 | `description` | Optional asset description, used in [auto-generated docs](#custom-docs).                                                                                                                             |