diff --git a/src/core/server/saved_objects/migrations/kibana/kibana_migrator.test.ts b/src/core/server/saved_objects/migrations/kibana/kibana_migrator.test.ts
index 7237d62dca6e2..9fc8afd356043 100644
--- a/src/core/server/saved_objects/migrations/kibana/kibana_migrator.test.ts
+++ b/src/core/server/saved_objects/migrations/kibana/kibana_migrator.test.ts
@@ -84,6 +84,30 @@ describe('KibanaMigrator', () => {
       const migrationResults = await new KibanaMigrator({ kbnServer }).awaitMigration();
       expect(migrationResults.length).toEqual(2);
     });
+
+    it('only handles and deletes index templates once', async () => {
+      const { kbnServer } = mockKbnServer();
+      const clusterStub = jest.fn<any, any>(() => ({ status: 404 }));
+      const waitUntilReady = jest.fn(async () => undefined);
+
+      kbnServer.server.plugins.elasticsearch = {
+        waitUntilReady,
+        getCluster() {
+          return {
+            callWithInternalUser: clusterStub,
+          };
+        },
+      };
+
+      await new KibanaMigrator({ kbnServer }).awaitMigration();
+
+      // callCluster with "cat.templates" is called by "deleteIndexTemplates" function
+      // and should only be done once
+      const callClusterCommands = clusterStub.mock.calls
+        .map(([callClusterPath]) => callClusterPath)
+        .filter(callClusterPath => callClusterPath === 'cat.templates');
+      expect(callClusterCommands.length).toBe(1);
+    });
   });
 });
 
diff --git a/src/core/server/saved_objects/migrations/kibana/kibana_migrator.ts b/src/core/server/saved_objects/migrations/kibana/kibana_migrator.ts
index f51c15f882a4e..0c2cb768fc011 100644
--- a/src/core/server/saved_objects/migrations/kibana/kibana_migrator.ts
+++ b/src/core/server/saved_objects/migrations/kibana/kibana_migrator.ts
@@ -93,8 +93,9 @@ export class KibanaMigrator {
     await server.plugins.elasticsearch.waitUntilReady();
 
     const config = server.config();
+    const kibanaIndexName = config.get('kibana.index');
     const indexMap = createIndexMap(
-      config.get('kibana.index'),
+      kibanaIndexName,
       this.kbnServer.uiExports.savedObjectSchemas,
       this.mappingProperties
     );
@@ -110,7 +111,9 @@ export class KibanaMigrator {
         pollInterval: config.get('migrations.pollInterval'),
         scrollDuration: config.get('migrations.scrollDuration'),
         serializer: this.serializer,
-        obsoleteIndexTemplatePattern: 'kibana_index_template*',
+        // Only necessary for the migrator of the kibana index.
+        obsoleteIndexTemplatePattern:
+          index === kibanaIndexName ? 'kibana_index_template*' : undefined,
         convertToAliasScript: indexMap[index].script,
       });
     });