diff --git a/core/src/main/scala/org/apache/spark/storage/BlockManagerMasterEndpoint.scala b/core/src/main/scala/org/apache/spark/storage/BlockManagerMasterEndpoint.scala
index 2df26f3530ef..6f043da76d5f 100644
--- a/core/src/main/scala/org/apache/spark/storage/BlockManagerMasterEndpoint.scala
+++ b/core/src/main/scala/org/apache/spark/storage/BlockManagerMasterEndpoint.scala
@@ -117,15 +117,20 @@ class BlockManagerMasterEndpoint(
 
     case _updateBlockInfo @
         UpdateBlockInfo(blockManagerId, blockId, storageLevel, deserializedSize, size) =>
-      val response = updateBlockInfo(blockManagerId, blockId, storageLevel, deserializedSize, size)
 
-      response.foreach { isSuccess =>
+      @inline def handleResult(success: Boolean): Unit = {
         // SPARK-30594: we should not post `SparkListenerBlockUpdated` when updateBlockInfo
         // returns false since the block info would be updated again later.
-        if (isSuccess) {
+        if (success) {
           listenerBus.post(SparkListenerBlockUpdated(BlockUpdatedInfo(_updateBlockInfo)))
         }
-        context.reply(isSuccess)
+        context.reply(success)
+      }
+
+      if (blockId.isShuffle) {
+        updateShuffleBlockInfo(blockId, blockManagerId).foreach(handleResult)
+      } else {
+        handleResult(updateBlockInfo(blockManagerId, blockId, storageLevel, deserializedSize, size))
       }
 
     case GetLocations(blockId) =>
@@ -571,46 +576,54 @@ class BlockManagerMasterEndpoint(
     id
   }
 
+ private def updateShuffleBlockInfo(blockId: BlockId, blockManagerId: BlockManagerId)
+    : Future[Boolean] = {
+   blockId match {
+     case ShuffleIndexBlockId(shuffleId, mapId, _) =>
+       // SPARK-36782: Invoke `MapOutputTracker.updateMapOutput` within the thread
+       // `dispatcher-BlockManagerMaster` could lead to the deadlock when
+       // `MapOutputTracker.serializeOutputStatuses` broadcasts the serialized mapstatues under
+       // the acquired write lock. The broadcast block would report its status to
+       // `BlockManagerMasterEndpoint`, while the `BlockManagerMasterEndpoint` is occupied by
+       // `updateMapOutput` since it's waiting for the write lock. Thus, we use `Future` to call
+       // `updateMapOutput` in a separate thread to avoid the deadlock.
+       Future {
+         // We need to update this at index file because there exists the index-only block
+         logDebug(s"Received shuffle index block update for ${shuffleId} ${mapId}, updating.")
+         mapOutputTracker.updateMapOutput(shuffleId, mapId, blockManagerId)
+         true
+       }
+     case ShuffleDataBlockId(shuffleId: Int, mapId: Long, reduceId: Int) =>
+       logDebug(s"Received shuffle data block update for ${shuffleId} ${mapId}, ignore.")
+       Future.successful(true)
+     case _ =>
+       logDebug(s"Unexpected shuffle block type ${blockId}" +
+         s"as ${blockId.getClass().getSimpleName()}")
+       Future.successful(false)
+   }
+ }
+
   private def updateBlockInfo(
       blockManagerId: BlockManagerId,
       blockId: BlockId,
       storageLevel: StorageLevel,
       memSize: Long,
-      diskSize: Long): Future[Boolean] = {
+      diskSize: Long): Boolean = {
     logDebug(s"Updating block info on master ${blockId} for ${blockManagerId}")
 
-    if (blockId.isShuffle) {
-      blockId match {
-        case ShuffleIndexBlockId(shuffleId, mapId, _) =>
-          // We need to update this at index file because there exists the index-only block
-          return Future {
-            logDebug(s"Received shuffle index block update for ${shuffleId} ${mapId}, updating.")
-            mapOutputTracker.updateMapOutput(shuffleId, mapId, blockManagerId)
-            true
-          }
-        case ShuffleDataBlockId(shuffleId: Int, mapId: Long, reduceId: Int) =>
-          logDebug(s"Received shuffle data block update for ${shuffleId} ${mapId}, ignore.")
-          return Future.successful(true)
-        case _ =>
-          logDebug(s"Unexpected shuffle block type ${blockId}" +
-            s"as ${blockId.getClass().getSimpleName()}")
-          return Future.successful(false)
-      }
-    }
-
     if (!blockManagerInfo.contains(blockManagerId)) {
       if (blockManagerId.isDriver && !isLocal) {
         // We intentionally do not register the master (except in local mode),
         // so we should not indicate failure.
-        return Future.successful(true)
+        return true
       } else {
-        return Future.successful(false)
+        return false
       }
     }
 
     if (blockId == null) {
       blockManagerInfo(blockManagerId).updateLastSeenMs()
-      return Future.successful(true)
+      return true
     }
 
     blockManagerInfo(blockManagerId).updateBlockInfo(blockId, storageLevel, memSize, diskSize)
@@ -642,7 +655,7 @@ class BlockManagerMasterEndpoint(
     if (locations.size == 0) {
       blockLocations.remove(blockId)
     }
-    Future.successful(true)
+    true
   }
 
   private def getLocations(blockId: BlockId): Seq[BlockManagerId] = {