diff --git a/server/src/main/java/org/elasticsearch/repositories/blobstore/BlobStoreRepository.java b/server/src/main/java/org/elasticsearch/repositories/blobstore/BlobStoreRepository.java
index 498b5bdbb49..8333b9cf029 100644
--- a/server/src/main/java/org/elasticsearch/repositories/blobstore/BlobStoreRepository.java
+++ b/server/src/main/java/org/elasticsearch/repositories/blobstore/BlobStoreRepository.java
@@ -736,6 +736,9 @@ public abstract class BlobStoreRepository extends AbstractLifecycleComponent imp
                         return false;
                     }
                     return allSnapshotIds.contains(foundUUID) == false;
+                } else if (blob.startsWith(INDEX_FILE_PREFIX)) {
+                    // TODO: Include the current generation here once we remove keeping index-(N-1) around from #writeIndexGen
+                    return repositoryData.getGenId() > Long.parseLong(blob.substring(INDEX_FILE_PREFIX.length()));
                 }
                 return false;
             }
diff --git a/server/src/test/java/org/elasticsearch/repositories/blobstore/BlobStoreRepositoryCleanupIT.java b/server/src/test/java/org/elasticsearch/repositories/blobstore/BlobStoreRepositoryCleanupIT.java
index 7ee49e53e26..fd195123fc0 100644
--- a/server/src/test/java/org/elasticsearch/repositories/blobstore/BlobStoreRepositoryCleanupIT.java
+++ b/server/src/test/java/org/elasticsearch/repositories/blobstore/BlobStoreRepositoryCleanupIT.java
@@ -19,6 +19,7 @@
 package org.elasticsearch.repositories.blobstore;
 
 import org.elasticsearch.action.ActionRunnable;
+import org.elasticsearch.action.admin.cluster.snapshots.create.CreateSnapshotResponse;
 import org.elasticsearch.action.support.PlainActionFuture;
 import org.elasticsearch.cluster.RepositoryCleanupInProgress;
 import org.elasticsearch.common.settings.Settings;
@@ -26,13 +27,16 @@ import org.elasticsearch.common.unit.ByteSizeUnit;
 import org.elasticsearch.common.unit.TimeValue;
 import org.elasticsearch.repositories.RepositoriesService;
 import org.elasticsearch.snapshots.AbstractSnapshotIntegTestCase;
+import org.elasticsearch.snapshots.SnapshotState;
 import org.elasticsearch.test.ESIntegTestCase;
 
 import java.io.ByteArrayInputStream;
+import java.util.concurrent.ExecutionException;
 import java.util.concurrent.TimeUnit;
 
 import static org.elasticsearch.test.hamcrest.ElasticsearchAssertions.assertAcked;
 import static org.elasticsearch.test.hamcrest.ElasticsearchAssertions.assertThrows;
+import static org.hamcrest.Matchers.is;
 
 @ESIntegTestCase.ClusterScope(scope = ESIntegTestCase.Scope.TEST, numDataNodes = 0)
 public class BlobStoreRepositoryCleanupIT extends AbstractSnapshotIntegTestCase {
@@ -107,4 +111,40 @@ public class BlobStoreRepositoryCleanupIT extends AbstractSnapshotIntegTestCase
         waitForBlock(masterNode, repoName, TimeValue.timeValueSeconds(60));
         return masterNode;
     }
+
+    public void testCleanupOldIndexN() throws ExecutionException, InterruptedException {
+        internalCluster().startNodes(Settings.EMPTY);
+
+        final String repoName = "test-repo";
+        logger.info("-->  creating repository");
+        assertAcked(client().admin().cluster().preparePutRepository(repoName).setType("fs").setSettings(Settings.builder()
+            .put("location", randomRepoPath())
+            .put("compress", randomBoolean())
+            .put("chunk_size", randomIntBetween(100, 1000), ByteSizeUnit.BYTES)));
+
+        logger.info("--> create three snapshots");
+        for (int i = 0; i < 3; ++i) {
+            CreateSnapshotResponse createSnapshotResponse = client().admin().cluster().prepareCreateSnapshot(repoName, "test-snap-" + i)
+                .setWaitForCompletion(true).get();
+            assertThat(createSnapshotResponse.getSnapshotInfo().state(), is(SnapshotState.SUCCESS));
+        }
+
+        final RepositoriesService service = internalCluster().getInstance(RepositoriesService.class, internalCluster().getMasterName());
+        final BlobStoreRepository repository = (BlobStoreRepository) service.repository(repoName);
+
+        logger.info("--> write two outdated index-N blobs");
+        for (int i = 0; i < 2; ++i) {
+            final PlainActionFuture<Void> createOldIndexNFuture = PlainActionFuture.newFuture();
+            final int generation = i;
+            repository.threadPool().generic().execute(ActionRunnable.run(createOldIndexNFuture, () -> repository.blobStore()
+                .blobContainer(repository.basePath()).writeBlob(BlobStoreRepository.INDEX_FILE_PREFIX + generation,
+                    new ByteArrayInputStream(new byte[1]), 1, true)));
+            createOldIndexNFuture.get();
+        }
+
+        logger.info("--> cleanup repository");
+        client().admin().cluster().prepareCleanupRepository(repoName).get();
+
+        BlobStoreTestUtil.assertConsistency(repository, repository.threadPool().generic());
+    }
 }