diff --git a/django/db/models/expressions.py b/django/db/models/expressions.py
index f79865d153..8e84be68cf 100644
--- a/django/db/models/expressions.py
+++ b/django/db/models/expressions.py
@@ -836,6 +836,7 @@ class Case(Expression):
         return c
 
     def as_sql(self, compiler, connection, template=None, case_joiner=None, **extra_context):
+        from django.db.models.sql.datastructures import EmptyResultSet
         connection.ops.check_expression_support(self)
         if not self.cases:
             return compiler.compile(self.default)
@@ -844,12 +845,17 @@ class Case(Expression):
         case_parts = []
         sql_params = []
         for case in self.cases:
-            case_sql, case_params = compiler.compile(case)
+            try:
+                case_sql, case_params = compiler.compile(case)
+            except EmptyResultSet:
+                continue
             case_parts.append(case_sql)
             sql_params.extend(case_params)
+        default_sql, default_params = compiler.compile(self.default)
+        if not case_parts:
+            return default_sql, default_params
         case_joiner = case_joiner or self.case_joiner
         template_params['cases'] = case_joiner.join(case_parts)
-        default_sql, default_params = compiler.compile(self.default)
         template_params['default'] = default_sql
         sql_params.extend(default_params)
         template = template or template_params.get('template', self.template)
diff --git a/tests/expressions_case/tests.py b/tests/expressions_case/tests.py
index 30e8a704ae..c3b754fcae 100644
--- a/tests/expressions_case/tests.py
+++ b/tests/expressions_case/tests.py
@@ -275,6 +275,16 @@ class CaseExpressionTests(TestCase):
             [1, 4, 3, 3, 3, 2, 2]
         )
 
+    def test_annotate_with_empty_when(self):
+        objects = CaseTestModel.objects.annotate(
+            selected=Case(
+                When(pk__in=[], then=Value('selected')),
+                default=Value('not selected'), output_field=models.CharField()
+            )
+        )
+        self.assertEqual(len(objects), CaseTestModel.objects.count())
+        self.assertTrue(all(obj.selected == 'not selected' for obj in objects))
+
     def test_combined_expression(self):
         self.assertQuerysetEqual(
             CaseTestModel.objects.annotate(