diff --git a/pandas/compat/_optional.py b/pandas/compat/_optional.py
index 3775a47d44521..def881b8fd863 100644
--- a/pandas/compat/_optional.py
+++ b/pandas/compat/_optional.py
@@ -1,6 +1,8 @@
 import distutils.version
 import importlib
+import sys
 import types
+from typing import Optional
 import warnings
 
 # Update install.rst when updating versions!
@@ -58,7 +60,11 @@ def _get_version(module: types.ModuleType) -> str:
 
 
 def import_optional_dependency(
-    name: str, extra: str = "", raise_on_missing: bool = True, on_version: str = "raise"
+    name: str,
+    extra: str = "",
+    raise_on_missing: bool = True,
+    on_version: str = "raise",
+    min_version: Optional[str] = None,
 ):
     """
     Import an optional dependency.
@@ -70,8 +76,7 @@ def import_optional_dependency(
     Parameters
     ----------
     name : str
-        The module name. This should be top-level only, so that the
-        version may be checked.
+        The module name.
     extra : str
         Additional text to include in the ImportError message.
     raise_on_missing : bool, default True
@@ -85,7 +90,9 @@ def import_optional_dependency(
         * ignore: Return the module, even if the version is too old.
           It's expected that users validate the version locally when
           using ``on_version="ignore"`` (see. ``io/html.py``)
-
+    min_version : str, default None
+        Specify a minimum version that is different from the global pandas
+        minimum version required.
     Returns
     -------
     maybe_module : Optional[ModuleType]
@@ -110,13 +117,20 @@ def import_optional_dependency(
         else:
             return None
 
-    minimum_version = VERSIONS.get(name)
+    # Handle submodules: if we have submodule, grab parent module from sys.modules
+    parent = name.split(".")[0]
+    if parent != name:
+        install_name = parent
+        module_to_get = sys.modules[install_name]
+    else:
+        module_to_get = module
+    minimum_version = min_version if min_version is not None else VERSIONS.get(parent)
     if minimum_version:
-        version = _get_version(module)
+        version = _get_version(module_to_get)
         if distutils.version.LooseVersion(version) < minimum_version:
             assert on_version in {"warn", "raise", "ignore"}
             msg = (
-                f"Pandas requires version '{minimum_version}' or newer of '{name}' "
+                f"Pandas requires version '{minimum_version}' or newer of '{parent}' "
                 f"(version '{version}' currently installed)."
             )
             if on_version == "warn":
diff --git a/pandas/tests/test_optional_dependency.py b/pandas/tests/test_optional_dependency.py
index e5ed69b7703b1..304ec124ac8c5 100644
--- a/pandas/tests/test_optional_dependency.py
+++ b/pandas/tests/test_optional_dependency.py
@@ -33,6 +33,10 @@ def test_bad_version(monkeypatch):
     with pytest.raises(ImportError, match=match):
         import_optional_dependency("fakemodule")
 
+    # Test min_version parameter
+    result = import_optional_dependency("fakemodule", min_version="0.8")
+    assert result is module
+
     with tm.assert_produces_warning(UserWarning):
         result = import_optional_dependency("fakemodule", on_version="warn")
     assert result is None
@@ -42,6 +46,31 @@ def test_bad_version(monkeypatch):
     assert result is module
 
 
+def test_submodule(monkeypatch):
+    # Create a fake module with a submodule
+    name = "fakemodule"
+    module = types.ModuleType(name)
+    module.__version__ = "0.9.0"
+    sys.modules[name] = module
+    sub_name = "submodule"
+    submodule = types.ModuleType(sub_name)
+    setattr(module, sub_name, submodule)
+    sys.modules[f"{name}.{sub_name}"] = submodule
+    monkeypatch.setitem(VERSIONS, name, "1.0.0")
+
+    match = "Pandas requires .*1.0.0.* of .fakemodule.*'0.9.0'"
+    with pytest.raises(ImportError, match=match):
+        import_optional_dependency("fakemodule.submodule")
+
+    with tm.assert_produces_warning(UserWarning):
+        result = import_optional_dependency("fakemodule.submodule", on_version="warn")
+    assert result is None
+
+    module.__version__ = "1.0.0"  # exact match is OK
+    result = import_optional_dependency("fakemodule.submodule")
+    assert result is submodule
+
+
 def test_no_version_raises(monkeypatch):
     name = "fakemodule"
     module = types.ModuleType(name)