diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 920919755dc23..10dd73d811b5e 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -69,7 +69,8 @@ Backwards incompatible API changes
 Deprecations
 ~~~~~~~~~~~~
 
--
+- Access to the ``pandas.core`` submodule is now deprecated, and the module will be moving to ``pandas._core`` in the future.
+  Please import all classes/methods from the top level pandas namespace instead.
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/__init__.py b/pandas/__init__.py
index d526531b159b2..6d16ec77237af 100644
--- a/pandas/__init__.py
+++ b/pandas/__init__.py
@@ -190,6 +190,10 @@
 # TODO: remove Panel compat in 1.0
 if pandas.compat.PY37:
 
+    import pandas.core as _core
+
+    del pandas.core
+
     def __getattr__(name):
         import warnings
 
@@ -256,6 +260,18 @@ class Panel:
 
             return _SparseArray
 
+        elif name == "core":
+
+            warnings.warn(
+                "The pandas.core module is private and access "
+                "will be moved to pandas._core in a future version. "
+                f"You should import directly from the pandas namespace instead",
+                FutureWarning,
+                stacklevel=2,
+            )
+
+            return _core
+
         raise AttributeError(f"module 'pandas' has no attribute '{name}'")
 
 
@@ -360,6 +376,27 @@ def __new__(cls, *args, **kwargs):
 
     SparseArray = __SparseArraySub
 
+    class __core:
+        def __init__(self):
+            import pandas.core as core
+            import warnings
+
+            self._core = core
+            self._warnings = warnings
+
+        def __getattr__(self, item):
+            attr = getattr(self._core, item)
+            self._warnings.warn(
+                "The pandas.core module is private and access "
+                "will be moved to pandas._core in a future version. "
+                f"You should import pandas.{item} directly instead",
+                FutureWarning,
+                stacklevel=2,
+            )
+            return attr
+
+    _core: __core = __core()  # type: ignore
+    core: __core = __core()
 
 # module level doc-string
 __doc__ = """
diff --git a/pandas/tests/api/test_api.py b/pandas/tests/api/test_api.py
index 406d5f055797d..42b9f8bcbc04c 100644
--- a/pandas/tests/api/test_api.py
+++ b/pandas/tests/api/test_api.py
@@ -33,7 +33,6 @@ class TestPDApi(Base):
         "api",
         "arrays",
         "compat",
-        "core",
         "errors",
         "pandas",
         "plotting",
@@ -46,7 +45,7 @@ class TestPDApi(Base):
     ]
 
     # these are already deprecated; awaiting removal
-    deprecated_modules: List[str] = ["np", "datetime"]
+    deprecated_modules: List[str] = ["np", "datetime", "core"]
 
     # misc
     misc = ["IndexSlice", "NaT", "NA"]
@@ -190,6 +189,7 @@ class TestPDApi(Base):
     # private modules in pandas namespace
     private_modules = [
         "_config",
+        "_core",
         "_hashtable",
         "_lib",
         "_libs",
@@ -241,11 +241,11 @@ def test_depr(self):
                 deprecated = getattr(pd, depr)
                 if not compat.PY37:
                     if depr == "datetime":
-                        deprecated.__getattr__(dir(pd.datetime.datetime)[-1])
+                        deprecated.__getattr__(dir(pd.datetime.datetime)[0])
                     elif depr == "SparseArray":
                         deprecated([])
                     else:
-                        deprecated.__getattr__(dir(deprecated)[-1])
+                        deprecated.__getattr__(dir(deprecated)[0])
 
 
 def test_datetime():