diff --git a/django/db/backends/__init__.py b/django/db/backends/__init__.py
index 55ed1f0a16..480b81be7f 100644
--- a/django/db/backends/__init__.py
+++ b/django/db/backends/__init__.py
@@ -442,9 +442,14 @@ class BaseDatabaseWrapper(object):
     def is_usable(self):
         """
         Tests if the database connection is usable.
+
         This function may assume that self.connection is not None.
+
+        Actual implementations should take care not to raise exceptions
+        as that may prevent Django from recycling unusable connections.
         """
-        raise NotImplementedError
+        raise NotImplementedError(
+            "subclasses of BaseDatabaseWrapper may require an is_usable() method")
 
     def close_if_unusable_or_obsolete(self):
         """
diff --git a/django/db/backends/mysql/base.py b/django/db/backends/mysql/base.py
index d760418aaf..87401f2da9 100644
--- a/django/db/backends/mysql/base.py
+++ b/django/db/backends/mysql/base.py
@@ -517,7 +517,7 @@ class DatabaseWrapper(BaseDatabaseWrapper):
     def is_usable(self):
         try:
             self.connection.ping()
-        except DatabaseError:
+        except Database.Error:
             return False
         else:
             return True
diff --git a/django/db/backends/oracle/base.py b/django/db/backends/oracle/base.py
index 46f89ffd2f..7610045f67 100644
--- a/django/db/backends/oracle/base.py
+++ b/django/db/backends/oracle/base.py
@@ -642,7 +642,7 @@ class DatabaseWrapper(BaseDatabaseWrapper):
             else:
                 # Use a cx_Oracle cursor directly, bypassing Django's utilities.
                 self.connection.cursor().execute("SELECT 1 FROM DUAL")
-        except DatabaseError:
+        except Database.Error:
             return False
         else:
             return True
diff --git a/django/db/backends/postgresql_psycopg2/base.py b/django/db/backends/postgresql_psycopg2/base.py
index ec2b71c3a1..23da101d01 100644
--- a/django/db/backends/postgresql_psycopg2/base.py
+++ b/django/db/backends/postgresql_psycopg2/base.py
@@ -190,7 +190,7 @@ class DatabaseWrapper(BaseDatabaseWrapper):
         try:
             # Use a psycopg cursor directly, bypassing Django's utilities.
             self.connection.cursor().execute("SELECT 1")
-        except DatabaseError:
+        except Database.Error:
             return False
         else:
             return True
diff --git a/tests/backends/tests.py b/tests/backends/tests.py
index 52897e4732..9f8d14279e 100644
--- a/tests/backends/tests.py
+++ b/tests/backends/tests.py
@@ -612,6 +612,37 @@ class BackendTestCase(TestCase):
             cursor.execute(query)
 
 
+class IsUsableTests(TransactionTestCase):
+    # Avoid using a regular TestCase because Django really dislikes closing
+    # the database connection inside a transaction at this point (#21202).
+
+    available_apps = []
+
+    # Unfortunately with sqlite3 the in-memory test database cannot be closed.
+    @skipUnlessDBFeature('test_db_allows_multiple_connections')
+    def test_is_usable_after_database_disconnects(self):
+        """
+        Test that is_usable() doesn't crash when the database disconnects.
+
+        Regression for #21553.
+        """
+        # Open a connection to the database.
+        with connection.cursor():
+            pass
+        # Emulate a connection close by the database.
+        connection._close()
+        # Even then is_usable() should not raise an exception.
+        try:
+            self.assertFalse(connection.is_usable())
+        finally:
+            # Clean up the mess created by connection._close(). Since the
+            # connection is already closed, this crashes on some backends.
+            try:
+                connection.close()
+            except Exception:
+                pass
+
+
 # We don't make these tests conditional because that means we would need to
 # check and differentiate between:
 # * MySQL+InnoDB, MySQL+MYISAM (something we currently can't do).