diff --git a/django/db/models/sql/query.py b/django/db/models/sql/query.py
index 403968e1183..df4de2a750b 100644
--- a/django/db/models/sql/query.py
+++ b/django/db/models/sql/query.py
@@ -123,12 +123,18 @@ class BaseQuery(object):
         obj_dict['related_select_fields'] = []
         obj_dict['related_select_cols'] = []
         del obj_dict['connection']
+
+        # Fields can't be pickled, so we pickle the list of field names instead.
+        obj_dict['select_fields'] = [f.name for f in obj_dict['select_fields']]
         return obj_dict
 
     def __setstate__(self, obj_dict):
         """
         Unpickling support.
         """
+        # Rebuild list of field instances
+        obj_dict['select_fields'] = [obj_dict['model']._meta.get_field(name) for name in obj_dict['select_fields']]
+
         self.__dict__.update(obj_dict)
         # XXX: Need a better solution for this when multi-db stuff is
         # supported. It's the only class-reference to the module-level
diff --git a/tests/regressiontests/aggregation_regress/models.py b/tests/regressiontests/aggregation_regress/models.py
index a6f99a997d7..d1f1451e439 100644
--- a/tests/regressiontests/aggregation_regress/models.py
+++ b/tests/regressiontests/aggregation_regress/models.py
@@ -1,4 +1,6 @@
 # coding: utf-8
+import pickle
+
 from django.db import models
 from django.conf import settings
 
@@ -242,6 +244,19 @@ FieldError: Cannot resolve keyword 'foo' into field. Choices are: authors, conta
 >>> Book.objects.filter(id__in=ids)
 [<Book: Python Web Development with Django>]
 
+# Regression for #10197 -- Queries with aggregates can be pickled.
+# First check that pickling is possible at all. No crash = success
+>>> qs = Book.objects.annotate(num_authors=Count('authors'))
+>>> out = pickle.dumps(qs)
+
+# Then check that the round trip works.
+>>> query = qs.query.as_sql()[0]
+>>> select_fields = qs.query.select_fields
+>>> query2 = pickle.loads(pickle.dumps(qs))
+>>> query2.query.as_sql()[0] == query
+True
+>>> query2.query.select_fields = select_fields
+
 # Regression for #10199 - Aggregate calls clone the original query so the original query can still be used
 >>> books = Book.objects.all()
 >>> _ = books.aggregate(Avg('authors__age'))