diff --git a/packages/CodeQuality/src/Rector/Array_/CallableThisArrayToAnonymousFunctionRector.php b/packages/CodeQuality/src/Rector/Array_/CallableThisArrayToAnonymousFunctionRector.php
index a284fb6a40a..b48878f3a3a 100644
--- a/packages/CodeQuality/src/Rector/Array_/CallableThisArrayToAnonymousFunctionRector.php
+++ b/packages/CodeQuality/src/Rector/Array_/CallableThisArrayToAnonymousFunctionRector.php
@@ -10,6 +10,7 @@ use PhpParser\Node\Expr;
 use PhpParser\Node\Expr\Array_;
 use PhpParser\Node\Expr\Closure;
 use PhpParser\Node\Expr\ClosureUse;
+use PhpParser\Node\Expr\FuncCall;
 use PhpParser\Node\Expr\MethodCall;
 use PhpParser\Node\Expr\PropertyFetch;
 use PhpParser\Node\Expr\Variable;
@@ -133,7 +134,15 @@ PHP
         }
 
         // can be totally empty in case of "[, $value]"
-        return $array->items[0] === null;
+        if ($array->items[0] === null) {
+            return true;
+        }
+
+        if ($array->items[1] === null) {
+            return true;
+        }
+
+        return $this->isCallbackAtFunctionName($array, 'register_shutdown_function');
     }
 
     /**
@@ -241,4 +250,19 @@ PHP
 
         return $newParams;
     }
+
+    private function isCallbackAtFunctionName(Array_ $array, string $functionName): bool
+    {
+        $parentNode = $array->getAttribute(AttributeKey::PARENT_NODE);
+        if (! $parentNode instanceof Arg) {
+            return false;
+        }
+
+        $parentParentNode = $parentNode->getAttribute(AttributeKey::PARENT_NODE);
+        if (! $parentParentNode instanceof FuncCall) {
+            return false;
+        }
+
+        return $this->isName($parentParentNode, $functionName);
+    }
 }
diff --git a/packages/CodeQuality/tests/Rector/Array_/CallableThisArrayToAnonymousFunctionRector/Fixture/skip_error_handler_shutdown.php.inc b/packages/CodeQuality/tests/Rector/Array_/CallableThisArrayToAnonymousFunctionRector/Fixture/skip_error_handler_shutdown.php.inc
new file mode 100644
index 00000000000..8b5980c88ca
--- /dev/null
+++ b/packages/CodeQuality/tests/Rector/Array_/CallableThisArrayToAnonymousFunctionRector/Fixture/skip_error_handler_shutdown.php.inc
@@ -0,0 +1,15 @@
+<?php
+
+namespace Rector\CodeQuality\Tests\Rector\Array_\CallableThisArrayToAnonymousFunctionRector\Fixture;
+
+class SkipErrorHandlerShutdown
+{
+    public function run()
+    {
+        register_shutdown_function([$this, 'shutdown_function']);
+    }
+
+    public function shutdown_function()
+    {
+    }
+}