diff --git a/CHANGES.rst b/CHANGES.rst
index d2be0b4ff..7586d91c2 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -72,6 +72,9 @@ API Changes
   - The PSF photometry ``finder_results`` attribute is now returned as a
     ``QTable`` instead of a list of ``QTable``. [#1704]
 
+  - Deprecated the ``NonNormalizable`` custom warning class in favor of
+    ``AstropyUserWarning``. [#1710]
+
 - ``photutils.segmentation``
 
   - The ``SourceCatalog`` ``get_label`` and ``get_labels`` methods now
diff --git a/photutils/psf/models.py b/photutils/psf/models.py
index 269bce442..6858b6978 100644
--- a/photutils/psf/models.py
+++ b/photutils/psf/models.py
@@ -8,7 +8,8 @@
 
 import numpy as np
 from astropy.modeling import Fittable2DModel, Parameter
-from astropy.utils.exceptions import AstropyWarning
+from astropy.utils.decorators import deprecated
+from astropy.utils.exceptions import AstropyUserWarning, AstropyWarning
 
 from photutils.aperture import CircularAperture
 from photutils.utils._parameters import as_pair
@@ -17,6 +18,7 @@
            'IntegratedGaussianPRF', 'PRFAdapter']
 
 
+@deprecated('1.11.0', alternative='AstropyUserWarning')
 class NonNormalizable(AstropyWarning):
     """
     Used to indicate that a :py:class:`FittableImageModel` model is
@@ -229,7 +231,7 @@ def _compute_normalization(self, normalize=True):
                 self._normalization_status = 1
                 warnings.warn('Overflow encountered while computing '
                               'normalization constant. Normalization '
-                              'constant will be set to 1.', NonNormalizable)
+                              'constant will be set to 1.', AstropyUserWarning)
 
         else:
             self._normalization_status = 2
@@ -572,7 +574,7 @@ def _compute_normalization(self, normalize=True):
                 self._img_norm = 1
                 warnings.warn('Overflow encountered while computing '
                               'normalization constant. Normalization '
-                              'constant will be set to 1.', NonNormalizable)
+                              'constant will be set to 1.', AstropyUserWarning)
         else:
             self._normalization_status = 2