diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index bbcb49cb6f129..fe88cf93886ce 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -682,6 +682,7 @@ Deprecations
 - Deprecated passing arguments as positional in :meth:`DataFrame.clip` and :meth:`Series.clip` (other than ``"upper"`` and ``"lower"``) (:issue:`41485`)
 - Deprecated special treatment of lists with first element a Categorical in the :class:`DataFrame` constructor; pass as ``pd.DataFrame({col: categorical, ...})`` instead (:issue:`38845`)
 - Deprecated passing arguments as positional (except for ``"method"``) in :meth:`DataFrame.interpolate` and :meth:`Series.interpolate` (:issue:`41485`)
+- Deprecated passing arguments as positional in :meth:`DataFrame.dropna` and :meth:`Series.dropna` (:issue:`41485`)
 - Deprecated passing arguments as positional in :meth:`DataFrame.set_index` (other than ``"keys"``) (:issue:`41485`)
 - Deprecated passing arguments as positional (except for ``"levels"``) in :meth:`MultiIndex.set_levels` (:issue:`41485`)
 - Deprecated passing arguments as positional in :meth:`DataFrame.sort_index` and :meth:`Series.sort_index` (:issue:`41485`)
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 35b55f68d0240..748a103a89965 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5835,6 +5835,7 @@ def notna(self) -> DataFrame:
     def notnull(self) -> DataFrame:
         return ~self.isna()
 
+    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self"])
     def dropna(
         self,
         axis: Axis = 0,
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 0975b1013e8d2..ce38e1ccb2613 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -5093,6 +5093,7 @@ def notna(self) -> Series:
     def notnull(self) -> Series:
         return super().notnull()
 
+    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self"])
     def dropna(self, axis=0, inplace=False, how=None):
         """
         Return a new Series with missing values removed.
diff --git a/pandas/tests/frame/methods/test_dropna.py b/pandas/tests/frame/methods/test_dropna.py
index b671bb1afb27a..76a6f3aa25362 100644
--- a/pandas/tests/frame/methods/test_dropna.py
+++ b/pandas/tests/frame/methods/test_dropna.py
@@ -231,3 +231,15 @@ def test_dropna_with_duplicate_columns(self):
 
         result = df.dropna(subset=["A", "C"], how="all")
         tm.assert_frame_equal(result, expected)
+
+    def test_dropna_pos_args_deprecation(self):
+        # https://github.com/pandas-dev/pandas/issues/41485
+        df = DataFrame({"a": [1, 2, 3]})
+        msg = (
+            r"In a future version of pandas all arguments of DataFrame\.dropna "
+            r"will be keyword-only"
+        )
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            result = df.dropna(1)
+        expected = DataFrame({"a": [1, 2, 3]})
+        tm.assert_frame_equal(result, expected)
diff --git a/pandas/tests/series/methods/test_dropna.py b/pandas/tests/series/methods/test_dropna.py
index 5bff7306fac33..0dab9271bfee5 100644
--- a/pandas/tests/series/methods/test_dropna.py
+++ b/pandas/tests/series/methods/test_dropna.py
@@ -101,3 +101,15 @@ def test_datetime64_tz_dropna(self):
         )
         assert result.dtype == "datetime64[ns, Asia/Tokyo]"
         tm.assert_series_equal(result, expected)
+
+    def test_dropna_pos_args_deprecation(self):
+        # https://github.com/pandas-dev/pandas/issues/41485
+        ser = Series([1, 2, 3])
+        msg = (
+            r"In a future version of pandas all arguments of Series\.dropna "
+            r"will be keyword-only"
+        )
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            result = ser.dropna(0)
+        expected = Series([1, 2, 3])
+        tm.assert_series_equal(result, expected)