diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 19db7dcb4b83e..41d519e0765dc 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -590,6 +590,7 @@ Deprecations
 - :func:`pandas.api.types.is_categorical` is deprecated and will be removed in a future version; use `:func:pandas.api.types.is_categorical_dtype` instead (:issue:`33385`)
 - :meth:`Index.get_value` is deprecated and will be removed in a future version (:issue:`19728`)
 - :meth:`DateOffset.__call__` is deprecated and will be removed in a future version, use ``offset + other`` instead (:issue:`34171`)
+- The ``squeeze`` keyword in the ``groupby`` function is deprecated and will be removed in a future version (:issue:`32380`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 2d181e826c2a9..01170320e5e31 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -42,6 +42,7 @@
 from pandas._config import get_option
 
 from pandas._libs import algos as libalgos, lib, properties
+from pandas._libs.lib import no_default
 from pandas._typing import (
     ArrayLike,
     Axes,
@@ -6253,12 +6254,24 @@ def groupby(
         as_index: bool = True,
         sort: bool = True,
         group_keys: bool = True,
-        squeeze: bool = False,
+        squeeze: bool = no_default,
         observed: bool = False,
         dropna: bool = True,
     ) -> "DataFrameGroupBy":
         from pandas.core.groupby.generic import DataFrameGroupBy
 
+        if squeeze is not no_default:
+            warnings.warn(
+                (
+                    "The `squeeze` parameter is deprecated and "
+                    "will be removed in a future version."
+                ),
+                FutureWarning,
+                stacklevel=2,
+            )
+        else:
+            squeeze = False
+
         if level is None and by is None:
             raise TypeError("You have to supply one of 'by' and 'level'")
         axis = self._get_axis_number(axis)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 5c7d0eae24cee..8aa8f8bb60654 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -7472,6 +7472,9 @@ def clip(
         squeeze : bool, default False
             Reduce the dimensionality of the return type if possible,
             otherwise return a consistent type.
+
+            .. deprecated:: 1.1.0
+
         observed : bool, default False
             This only applies if any of the groupers are Categoricals.
             If True: only show observed values for categorical groupers.
diff --git a/pandas/core/series.py b/pandas/core/series.py
index e107b66d33b1c..bc13d5376ec96 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -23,6 +23,7 @@
 from pandas._config import get_option
 
 from pandas._libs import lib, properties, reshape, tslibs
+from pandas._libs.lib import no_default
 from pandas._typing import ArrayLike, Axis, DtypeObj, IndexKeyFunc, Label, ValueKeyFunc
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import Appender, Substitution, doc
@@ -1642,12 +1643,24 @@ def groupby(
         as_index: bool = True,
         sort: bool = True,
         group_keys: bool = True,
-        squeeze: bool = False,
+        squeeze: bool = no_default,
         observed: bool = False,
         dropna: bool = True,
     ) -> "SeriesGroupBy":
         from pandas.core.groupby.generic import SeriesGroupBy
 
+        if squeeze is not no_default:
+            warnings.warn(
+                (
+                    "The `squeeze` parameter is deprecated and "
+                    "will be removed in a future version."
+                ),
+                FutureWarning,
+                stacklevel=2,
+            )
+        else:
+            squeeze = False
+
         if level is None and by is None:
             raise TypeError("You have to supply one of 'by' and 'level'")
         axis = self._get_axis_number(axis)
diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index c88d16e34eab8..a0d059fc8f83b 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -109,7 +109,8 @@ def test_groupby_return_type():
     def func(dataf):
         return dataf["val2"] - dataf["val2"].mean()
 
-    result = df1.groupby("val1", squeeze=True).apply(func)
+    with tm.assert_produces_warning(FutureWarning):
+        result = df1.groupby("val1", squeeze=True).apply(func)
     assert isinstance(result, Series)
 
     df2 = DataFrame(
@@ -124,12 +125,14 @@ def func(dataf):
     def func(dataf):
         return dataf["val2"] - dataf["val2"].mean()
 
-    result = df2.groupby("val1", squeeze=True).apply(func)
+    with tm.assert_produces_warning(FutureWarning):
+        result = df2.groupby("val1", squeeze=True).apply(func)
     assert isinstance(result, Series)
 
     # GH3596, return a consistent type (regression in 0.11 from 0.10.1)
     df = DataFrame([[1, 1], [1, 1]], columns=["X", "Y"])
-    result = df.groupby("X", squeeze=False).count()
+    with tm.assert_produces_warning(FutureWarning):
+        result = df.groupby("X", squeeze=False).count()
     assert isinstance(result, DataFrame)