diff --git a/server/src/main/java/org/elasticsearch/common/ReferenceDocs.java b/server/src/main/java/org/elasticsearch/common/ReferenceDocs.java
index 41faefaafc636..2567268415051 100644
--- a/server/src/main/java/org/elasticsearch/common/ReferenceDocs.java
+++ b/server/src/main/java/org/elasticsearch/common/ReferenceDocs.java
@@ -85,6 +85,7 @@ public enum ReferenceDocs {
     SECURE_SETTINGS,
     CLUSTER_SHARD_LIMIT,
     DEPLOY_CLOUD_DIFF_FROM_STATEFUL,
+    DELETE_INDEX_BLOCK,
     // this comment keeps the ';' on the next line so every entry above has a trailing ',' which makes the diff for adding new links cleaner
     ;
 
diff --git a/server/src/main/resources/org/elasticsearch/common/reference-docs-links.txt b/server/src/main/resources/org/elasticsearch/common/reference-docs-links.txt
index 50732d9289be5..5d8ae6c5498a5 100644
--- a/server/src/main/resources/org/elasticsearch/common/reference-docs-links.txt
+++ b/server/src/main/resources/org/elasticsearch/common/reference-docs-links.txt
@@ -47,3 +47,4 @@ ALLOCATION_EXPLAIN_MAX_RETRY                                    troubleshoot/ela
 SECURE_SETTINGS                                                 deploy-manage/security/secure-settings
 CLUSTER_SHARD_LIMIT                                             reference/elasticsearch/configuration-reference/miscellaneous-cluster-settings#cluster-shard-limit
 DEPLOY_CLOUD_DIFF_FROM_STATEFUL                                 deploy-manage/deploy/elastic-cloud/differences-from-other-elasticsearch-offerings
+DELETE_INDEX_BLOCK                                              api/doc/elasticsearch/operation/operation-indices-remove-block
diff --git a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/job/process/autodetect/JobModelSnapshotUpgrader.java b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/job/process/autodetect/JobModelSnapshotUpgrader.java
index d42eb8f748b51..d270e00f78e12 100644
--- a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/job/process/autodetect/JobModelSnapshotUpgrader.java
+++ b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/job/process/autodetect/JobModelSnapshotUpgrader.java
@@ -17,6 +17,7 @@
 import org.elasticsearch.action.support.WriteRequest;
 import org.elasticsearch.client.internal.Client;
 import org.elasticsearch.common.CheckedSupplier;
+import org.elasticsearch.common.ReferenceDocs;
 import org.elasticsearch.common.util.concurrent.AbstractRunnable;
 import org.elasticsearch.common.util.concurrent.EsRejectedExecutionException;
 import org.elasticsearch.common.util.concurrent.ThreadContext;
@@ -196,15 +197,21 @@ private void deleteOlderSnapshotDoc(SearchResponse searchResponse, Consumer<Exce
                     );
                 }
             }, e -> {
-                logger.warn(
-                    () -> format(
+                logger.warn(() -> {
+                    String baseMessage = format(
                         "[%s] [%s] failed to delete old snapshot [%s] result document",
                         jobId,
                         snapshotId,
                         ModelSizeStats.RESULT_TYPE_FIELD.getPreferredName()
-                    ),
-                    e
-                );
+                    );
+                    if (e instanceof org.elasticsearch.cluster.block.ClusterBlockException) {
+                        return baseMessage
+                            + ". Remove the write block from the results index to delete the model snapshot. See "
+                            + ReferenceDocs.DELETE_INDEX_BLOCK
+                            + " for details.";
+                    }
+                    return baseMessage;
+                }, e);
             }), () -> runAfter.accept(null)));
     }