diff --git a/astropy/io/fits/hdu/hdulist.py b/astropy/io/fits/hdu/hdulist.py
index 2d778a28f56a..808cf3e1da01 100644
--- a/astropy/io/fits/hdu/hdulist.py
+++ b/astropy/io/fits/hdu/hdulist.py
@@ -1,6 +1,5 @@
 # Licensed under a 3-clause BSD style license - see PYFITS.rst
 
-
 import gzip
 import itertools
 import os
@@ -354,7 +353,7 @@ def __setitem__(self, key, hdu):
             self._try_while_unread_hdus(super().__setitem__, _key, hdu)
         except IndexError:
             raise IndexError('Extension {} is out of bound or not found.'
-                            .format(key))
+                             .format(key))
 
         self._resize = True
         self._truncate = False
@@ -803,7 +802,7 @@ def flush(self, output_verify='fix', verbose=False):
 
         if self._file.mode not in ('append', 'update', 'ostream'):
             warnings.warn("Flush for '{}' mode is not supported."
-                         .format(self._file.mode), AstropyUserWarning)
+                          .format(self._file.mode), AstropyUserWarning)
             return
 
         save_backup = self._open_kwargs.get('save_backup', False)
@@ -1354,7 +1353,10 @@ def _flush_resize(self):
                 # flushing (on Windows--again, this is no problem on Linux).
                 for idx, mmap, arr in mmaps:
                     if mmap is not None:
-                        arr.data = self[idx].data.data
+                        # https://github.com/numpy/numpy/issues/8628
+                        with warnings.catch_warnings():
+                            warnings.simplefilter('ignore', category=DeprecationWarning)
+                            arr.data = self[idx].data.data
                 del mmaps  # Just to be sure
 
         else:
diff --git a/astropy/io/fits/tests/test_hdulist.py b/astropy/io/fits/tests/test_hdulist.py
index 5de58f5f6560..8c8c75d760a7 100644
--- a/astropy/io/fits/tests/test_hdulist.py
+++ b/astropy/io/fits/tests/test_hdulist.py
@@ -619,11 +619,6 @@ def test_update_with_truncated_header(self):
         with fits.open(self.temp('temp.fits')) as hdul:
             assert (hdul[0].data == data).all()
 
-    # This test used to fail on Windows - if it fails again in future, see
-    # https://github.com/astropy/astropy/issues/5797
-    # The warning appears on Windows but cannot be explicitly caught.
-    @pytest.mark.filterwarnings("ignore:Assigning the 'data' attribute is an "
-                                "inherently unsafe operation")
     def test_update_resized_header(self):
         """
         Test saving updates to a file where the header is one block smaller
diff --git a/astropy/io/fits/tests/test_image.py b/astropy/io/fits/tests/test_image.py
index 0273efbeba03..5bbf7759e715 100644
--- a/astropy/io/fits/tests/test_image.py
+++ b/astropy/io/fits/tests/test_image.py
@@ -239,11 +239,6 @@ def test_primary_with_extname(self):
         with fits.open(self.temp('test.fits')) as hdul:
             assert hdul[0].name == 'XPRIMARY2'
 
-    # This test used to fail on Windows - if it fails again in future, see
-    # https://github.com/astropy/astropy/issues/5797
-    # The warning appears on Windows but cannot be explicitly caught.
-    @pytest.mark.filterwarnings("ignore:Assigning the 'data' attribute is an "
-                                "inherently unsafe operation")
     def test_io_manipulation(self):
         # Get a keyword value.  An extension can be referred by name or by
         # number.  Both extension and keyword names are case insensitive.