diff --git a/tests/v1/core/test_async_scheduler.py b/tests/v1/core/test_async_scheduler.py
index e0645ed43..a77ae81ba 100644
--- a/tests/v1/core/test_async_scheduler.py
+++ b/tests/v1/core/test_async_scheduler.py
@@ -236,7 +236,7 @@ def test_prefix_caching_for_multi_turn():
         req._all_token_ids = req.prompt_token_ids.copy()
         req.all_token_ids = ConstantList(req._all_token_ids)
         req.block_hashes = []
-        req.block_hashes = req.get_hash_new_full_blocks()
+        req.update_block_hashes()
 
     # Schedule the next-turn requests.
     for req in next_turn_requests:
diff --git a/vllm/v1/core/sched/scheduler.py b/vllm/v1/core/sched/scheduler.py
index 90ca58441..aa3bc6e2c 100644
--- a/vllm/v1/core/sched/scheduler.py
+++ b/vllm/v1/core/sched/scheduler.py
@@ -982,10 +982,8 @@ class Scheduler(SchedulerInterface):
 
         session._all_token_ids.extend(update.prompt_token_ids or ())
         session.prompt_token_ids.extend(update.prompt_token_ids or ())
-        # Update block hashes for the new tokens
-        # (mirrors Request.append_output_token_ids)
-        if session.get_hash_new_full_blocks is not None:
-            session.block_hashes.extend(session.get_hash_new_full_blocks())
+        # Update block hashes for the new tokens.
+        session.update_block_hashes()
         session.num_prompt_tokens = len(session.prompt_token_ids)
         session.arrival_time = update.arrival_time
         session.sampling_params = update.sampling_params
diff --git a/vllm/v1/request.py b/vllm/v1/request.py
index 3b829875f..970b7e1eb 100644
--- a/vllm/v1/request.py
+++ b/vllm/v1/request.py
@@ -6,7 +6,6 @@ import time
 from collections import deque
 from collections.abc import Callable, Mapping
 from dataclasses import dataclass
-from functools import partial
 from typing import TYPE_CHECKING, Any
 
 import torch
@@ -164,10 +163,11 @@ class Request:
         self.num_external_computed_tokens = 0
 
         self.block_hashes: list[BlockHash] = []
-        self.get_hash_new_full_blocks: Callable[[], list[BlockHash]] | None = None
-        if block_hasher is not None:
-            self.get_hash_new_full_blocks = partial(block_hasher, self)
-            self.block_hashes = self.get_hash_new_full_blocks()
+        # Store the block hasher without binding self to avoid creating a
+        # reference cycle (Request -> partial -> Request) that prevents
+        # immediate garbage collection via reference counting.
+        self._block_hasher: Callable[[Request], list[BlockHash]] | None = block_hasher
+        self.update_block_hashes()
 
         self.skip_reading_prefix_cache = self.get_skip_reading_prefix_cache()
 
@@ -212,8 +212,12 @@ class Request:
             self._output_token_ids.extend(token_ids)
             self._all_token_ids.extend(token_ids)
 
-        if self.get_hash_new_full_blocks is not None:
-            self.block_hashes.extend(self.get_hash_new_full_blocks())
+        self.update_block_hashes()
+
+    def update_block_hashes(self) -> None:
+        """Compute block hashes for any new full blocks and append them."""
+        if self._block_hasher is not None:
+            self.block_hashes.extend(self._block_hasher(self))
 
     @property
     def use_structured_output(self) -> bool: