diff --git a/python/pyarrow/array.pxi b/python/pyarrow/array.pxi
index 20e778d068ff8..a693f45e967a5 100644
--- a/python/pyarrow/array.pxi
+++ b/python/pyarrow/array.pxi
@@ -121,6 +121,8 @@ cdef class Array:
             compatibility with other functionality like Parquet I/O which
             only supports milliseconds.
 
+            .. deprecated:: 0.7.0
+
         memory_pool: MemoryPool, optional
             Specific memory pool to use to allocate the resulting Arrow array.
 
diff --git a/python/pyarrow/table.pxi b/python/pyarrow/table.pxi
index 245371ffaa124..fc6099fe8430d 100644
--- a/python/pyarrow/table.pxi
+++ b/python/pyarrow/table.pxi
@@ -723,6 +723,9 @@ cdef class Table:
             Convert datetime columns to ms resolution. This is needed for
             compability with other functionality like Parquet I/O which
             only supports milliseconds.
+
+            .. deprecated:: 0.7.0
+
         schema : pyarrow.Schema, optional
             The expected schema of the Arrow Table. This can be used to
             indicate the type of columns if we cannot infer it automatically.
diff --git a/python/pyarrow/tests/test_convert_pandas.py b/python/pyarrow/tests/test_convert_pandas.py
index 52290d6d85533..64424341067bb 100644
--- a/python/pyarrow/tests/test_convert_pandas.py
+++ b/python/pyarrow/tests/test_convert_pandas.py
@@ -69,10 +69,10 @@ def tearDown(self):
         pass
 
     def _check_pandas_roundtrip(self, df, expected=None, nthreads=1,
-                                timestamps_to_ms=False, expected_schema=None,
+                                expected_schema=None,
                                 check_dtype=True, schema=None,
                                 check_index=False):
-        table = pa.Table.from_pandas(df, timestamps_to_ms=timestamps_to_ms,
+        table = pa.Table.from_pandas(df,
                                      schema=schema, preserve_index=check_index)
         result = table.to_pandas(nthreads=nthreads)
         if expected_schema:
@@ -92,9 +92,8 @@ def _check_series_roundtrip(self, s, type_=None):
         tm.assert_series_equal(s, result)
 
     def _check_array_roundtrip(self, values, expected=None, mask=None,
-                               timestamps_to_ms=False, type=None):
-        arr = pa.Array.from_pandas(values, timestamps_to_ms=timestamps_to_ms,
-                                   mask=mask, type=type)
+                               type=None):
+        arr = pa.Array.from_pandas(values, mask=mask, type=type)
         result = arr.to_pandas()
 
         values_nulls = pd.isnull(values)
@@ -332,21 +331,6 @@ def test_fixed_size_bytes_does_not_accept_varying_lengths(self):
             pa.Table.from_pandas(df, schema=schema)
 
     def test_timestamps_notimezone_no_nulls(self):
-        df = pd.DataFrame({
-            'datetime64': np.array([
-                '2007-07-13T01:23:34.123',
-                '2006-01-13T12:34:56.432',
-                '2010-08-13T05:46:57.437'],
-                dtype='datetime64[ms]')
-        })
-        field = pa.field('datetime64', pa.timestamp('ms'))
-        schema = pa.schema([field])
-        self._check_pandas_roundtrip(
-            df,
-            timestamps_to_ms=True,
-            expected_schema=schema,
-        )
-
         df = pd.DataFrame({
             'datetime64': np.array([
                 '2007-07-13T01:23:34.123456789',
@@ -357,7 +341,8 @@ def test_timestamps_notimezone_no_nulls(self):
         field = pa.field('datetime64', pa.timestamp('ns'))
         schema = pa.schema([field])
         self._check_pandas_roundtrip(
-            df, expected_schema=schema,
+            df,
+            expected_schema=schema,
         )
 
     def test_timestamps_to_ms_explicit_schema(self):
@@ -365,28 +350,15 @@ def test_timestamps_to_ms_explicit_schema(self):
         df = pd.DataFrame({'datetime': [datetime(2017, 1, 1)]})
         pa_type = pa.from_numpy_dtype(df['datetime'].dtype)
 
-        arr = pa.Array.from_pandas(df['datetime'], type=pa_type,
-                                   timestamps_to_ms=True)
+        with tm.assert_produces_warning(FutureWarning,
+                                        check_stacklevel=False):
+            arr = pa.Array.from_pandas(df['datetime'], type=pa_type,
+                                       timestamps_to_ms=True)
 
         tm.assert_almost_equal(df['datetime'].values.astype('M8[ms]'),
                                arr.to_pandas())
 
     def test_timestamps_notimezone_nulls(self):
-        df = pd.DataFrame({
-            'datetime64': np.array([
-                '2007-07-13T01:23:34.123',
-                None,
-                '2010-08-13T05:46:57.437'],
-                dtype='datetime64[ms]')
-        })
-        field = pa.field('datetime64', pa.timestamp('ms'))
-        schema = pa.schema([field])
-        self._check_pandas_roundtrip(
-            df,
-            timestamps_to_ms=True,
-            expected_schema=schema,
-        )
-
         df = pd.DataFrame({
             'datetime64': np.array([
                 '2007-07-13T01:23:34.123456789',
@@ -397,7 +369,8 @@ def test_timestamps_notimezone_nulls(self):
         field = pa.field('datetime64', pa.timestamp('ns'))
         schema = pa.schema([field])
         self._check_pandas_roundtrip(
-            df, expected_schema=schema,
+            df,
+            expected_schema=schema,
         )
 
     def test_timestamps_with_timezone(self):
@@ -410,7 +383,7 @@ def test_timestamps_with_timezone(self):
         })
         df['datetime64'] = (df['datetime64'].dt.tz_localize('US/Eastern')
                             .to_frame())
-        self._check_pandas_roundtrip(df, timestamps_to_ms=True)
+        self._check_pandas_roundtrip(df)
 
         self._check_series_roundtrip(df['datetime64'])
 
@@ -425,15 +398,8 @@ def test_timestamps_with_timezone(self):
         })
         df['datetime64'] = (df['datetime64'].dt.tz_localize('US/Eastern')
                             .to_frame())
-        self._check_pandas_roundtrip(df)
-
-    def test_timestamp_with_tz_to_pandas_type(self):
-        from pyarrow.compat import DatetimeTZDtype
 
-        tz = 'America/Los_Angeles'
-        t = pa.timestamp('ns', tz=tz)
-
-        assert t.to_pandas_dtype() == DatetimeTZDtype('ns', tz=tz)
+        self._check_pandas_roundtrip(df)
 
     def test_date_infer(self):
         df = pd.DataFrame({