diff --git a/rules-tests/DowngradePhp81/Rector/FuncCall/DowngradeHashAlgorithmXxHash/Fixture/fixture_fully_qualified_constant.php.inc b/rules-tests/DowngradePhp81/Rector/FuncCall/DowngradeHashAlgorithmXxHash/Fixture/fixture_fully_qualified_constant.php.inc
new file mode 100644
index 00000000..45542bc3
--- /dev/null
+++ b/rules-tests/DowngradePhp81/Rector/FuncCall/DowngradeHashAlgorithmXxHash/Fixture/fixture_fully_qualified_constant.php.inc
@@ -0,0 +1,27 @@
+<?php
+
+namespace Rector\Tests\DowngradePhp81\Rector\FuncCall\DowngradeHashAlgorithmXxHash\Fixture;
+
+final class FixtureFullyQualifiedConstant
+{
+    public function run()
+    {
+        return hash(\MHASH_XXH128, 'some-data-to-hash');
+    }
+}
+
+?>
+-----
+<?php
+
+namespace Rector\Tests\DowngradePhp81\Rector\FuncCall\DowngradeHashAlgorithmXxHash\Fixture;
+
+final class FixtureFullyQualifiedConstant
+{
+    public function run()
+    {
+        return hash('md5', 'some-data-to-hash');
+    }
+}
+
+?>
diff --git a/rules/DowngradePhp81/Rector/FuncCall/DowngradeHashAlgorithmXxHashRector.php b/rules/DowngradePhp81/Rector/FuncCall/DowngradeHashAlgorithmXxHashRector.php
index 435a9553..5a2304e8 100644
--- a/rules/DowngradePhp81/Rector/FuncCall/DowngradeHashAlgorithmXxHashRector.php
+++ b/rules/DowngradePhp81/Rector/FuncCall/DowngradeHashAlgorithmXxHashRector.php
@@ -24,13 +24,15 @@
 final class DowngradeHashAlgorithmXxHashRector extends AbstractRector
 {
     /**
-     * @var array<string, int>
+     * Constants are referenced by name, as the MHASH_* constants are deprecated since PHP 8.5
+     *
+     * @var array<string, string>
      */
     private const array HASH_ALGORITHMS_TO_DOWNGRADE = [
-        'xxh32' => MHASH_XXH32,
-        'xxh64' => MHASH_XXH64,
-        'xxh3' => MHASH_XXH3,
-        'xxh128' => MHASH_XXH128,
+        'xxh32' => 'MHASH_XXH32',
+        'xxh64' => 'MHASH_XXH64',
+        'xxh3' => 'MHASH_XXH3',
+        'xxh128' => 'MHASH_XXH128',
     ];
 
     private const string REPLACEMENT_ALGORITHM = 'md5';
@@ -167,7 +169,7 @@ private function getHashAlgorithm(array $args): ?string
 
     private function mapConstantToString(string $constant): string
     {
-        $mappedConstant = array_search(constant($constant), self::HASH_ALGORITHMS_TO_DOWNGRADE, true);
+        $mappedConstant = array_search(ltrim($constant, '\\'), self::HASH_ALGORITHMS_TO_DOWNGRADE, true);
 
         return $mappedConstant !== false ? $mappedConstant : $constant;
     }