diff --git a/django/db/models/fields/__init__.py b/django/db/models/fields/__init__.py
index e79f4acf6cc..0e72a09e594 100644
--- a/django/db/models/fields/__init__.py
+++ b/django/db/models/fields/__init__.py
@@ -2,6 +2,7 @@ import collections.abc
 import copy
 import datetime
 import decimal
+import math
 import operator
 import uuid
 import warnings
@@ -1539,6 +1540,12 @@ class DecimalField(Field):
         if value is None:
             return value
         if isinstance(value, float):
+            if math.isnan(value):
+                raise exceptions.ValidationError(
+                    self.error_messages['invalid'],
+                    code='invalid',
+                    params={'value': value},
+                )
             return self.context.create_decimal_from_float(value)
         try:
             return decimal.Decimal(value)
diff --git a/tests/model_fields/test_decimalfield.py b/tests/model_fields/test_decimalfield.py
index 2d96cfd4374..ea06ab9fa20 100644
--- a/tests/model_fields/test_decimalfield.py
+++ b/tests/model_fields/test_decimalfield.py
@@ -1,3 +1,4 @@
+import math
 from decimal import Decimal
 
 from django.core import validators
@@ -65,6 +66,13 @@ class DecimalFieldTests(TestCase):
         bd = BigD.objects.get(pk=bd.pk)
         self.assertEqual(bd.d, Decimal('12.9'))
 
+    def test_save_nan_invalid(self):
+        msg = '“nan” value must be a decimal number.'
+        with self.assertRaisesMessage(ValidationError, msg):
+            BigD.objects.create(d=float('nan'))
+        with self.assertRaisesMessage(ValidationError, msg):
+            BigD.objects.create(d=math.nan)
+
     def test_fetch_from_db_without_float_rounding(self):
         big_decimal = BigD.objects.create(d=Decimal('.100000000000000000000000000005'))
         big_decimal.refresh_from_db()