diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3571bf28e8..96c1cb84d1 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -127,6 +127,8 @@ The file documents changes to the PHP_CodeSniffer project.
     - Thanks to Dan Wallis (@fredden) for the patch
 - Fixed bug #3816 : PSR12/FileHeader: bug fix - false positives on PHP 8.2+ readonly classes
     - Thanks to Juliette Reinders Folmer (@jrfnl) for the patch
+- Fixed bug #3867 : Tokenizer/PHP: union type and intersection type operators were not correctly tokenized for static properties without explicit visibility
+    - Thanks to Juliette Reinders Folmer (@jrfnl) for the patch
 - Fixed bug #3877 : Filter names can be case-sensitive. The -h help text will now display the correct case for the available filters
     - Thanks to @simonsan for the patch
 - Fixed bug #3906 : Tokenizer/CSS: fixed a bug related to the unsupported slash comment syntax
diff --git a/src/Tokenizers/PHP.php b/src/Tokenizers/PHP.php
index 68a9ab76ec..5ca178bd04 100644
--- a/src/Tokenizers/PHP.php
+++ b/src/Tokenizers/PHP.php
@@ -2998,6 +2998,10 @@ protected function processAdditional()
                     continue;
                 }
 
+                if ($suspectedType === 'property or parameter') {
+                    unset($allowed[\T_STATIC]);
+                }
+
                 $typeTokenCount = 0;
                 $typeOperators  = [$i];
                 $confirmed      = false;
@@ -3030,6 +3034,7 @@ protected function processAdditional()
                     if ($suspectedType === 'property or parameter'
                         && (isset(Util\Tokens::$scopeModifiers[$this->tokens[$x]['code']]) === true
                         || $this->tokens[$x]['code'] === T_VAR
+                        || $this->tokens[$x]['code'] === T_STATIC
                         || $this->tokens[$x]['code'] === T_READONLY)
                     ) {
                         // This will also confirm constructor property promotion parameters, but that's fine.
diff --git a/tests/Core/File/GetMemberPropertiesTest.inc b/tests/Core/File/GetMemberPropertiesTest.inc
index 51d11c2f1a..441bd97772 100644
--- a/tests/Core/File/GetMemberPropertiesTest.inc
+++ b/tests/Core/File/GetMemberPropertiesTest.inc
@@ -210,7 +210,8 @@ $anon = class() {
 
     /* testPHP8UnionTypesIllegalTypes */
     // Intentional fatal error - types which are not allowed for properties, but that's not the concern of the method.
-    public callable|static|void $unionTypesIllegalTypes;
+    // Note: static is also not allowed as a type, but using static for a property type is not supported by the tokenizer.
+    public callable|void $unionTypesIllegalTypes;
 
     /* testPHP8UnionTypesNullable */
     // Intentional fatal error - nullability is not allowed with union types, but that's not the concern of the method.
diff --git a/tests/Core/File/GetMemberPropertiesTest.php b/tests/Core/File/GetMemberPropertiesTest.php
index 4fd5fb755b..272f3b2ef1 100644
--- a/tests/Core/File/GetMemberPropertiesTest.php
+++ b/tests/Core/File/GetMemberPropertiesTest.php
@@ -587,8 +587,7 @@ public function dataGetMemberProperties()
                     'scope_specified' => true,
                     'is_static'       => false,
                     'is_readonly'     => false,
-                    // Missing static, but that's OK as not an allowed syntax.
-                    'type'            => 'callable||void',
+                    'type'            => 'callable|void',
                     'nullable_type'   => false,
                 ],
             ],
diff --git a/tests/Core/Tokenizer/BitwiseOrTest.inc b/tests/Core/Tokenizer/BitwiseOrTest.inc
index 843f6c57d7..b758aba019 100644
--- a/tests/Core/Tokenizer/BitwiseOrTest.inc
+++ b/tests/Core/Tokenizer/BitwiseOrTest.inc
@@ -48,6 +48,9 @@ class TypeUnion
     /* testTypeUnionPropertyWithOnlyReadOnlyKeyword */
     readonly string|null $nullableString;
 
+    /* testTypeUnionPropertyWithOnlyStaticKeyword */
+    static Foo|Bar $obj;
+
     public function paramTypes(
         /* testTypeUnionParam1 */
         int|float $paramA /* testBitwiseOrParamDefaultValue */ = CONSTANT_A | CONSTANT_B,
diff --git a/tests/Core/Tokenizer/BitwiseOrTest.php b/tests/Core/Tokenizer/BitwiseOrTest.php
index aad4474049..81e10e01a9 100644
--- a/tests/Core/Tokenizer/BitwiseOrTest.php
+++ b/tests/Core/Tokenizer/BitwiseOrTest.php
@@ -110,6 +110,7 @@ public function dataTypeUnion()
             ['/* testTypeUnionPropertyWithStaticAndReadOnlyKeywords */'],
             ['/* testTypeUnionPropertyWithVarAndReadOnlyKeywords */'],
             ['/* testTypeUnionPropertyWithOnlyReadOnlyKeyword */'],
+            ['/* testTypeUnionPropertyWithOnlyStaticKeyword */'],
             ['/* testTypeUnionParam1 */'],
             ['/* testTypeUnionParam2 */'],
             ['/* testTypeUnionParam3 */'],
diff --git a/tests/Core/Tokenizer/TypeIntersectionTest.inc b/tests/Core/Tokenizer/TypeIntersectionTest.inc
index abf9b85ba8..ad421cba5a 100644
--- a/tests/Core/Tokenizer/TypeIntersectionTest.inc
+++ b/tests/Core/Tokenizer/TypeIntersectionTest.inc
@@ -36,6 +36,9 @@ class TypeIntersection
     /* testTypeIntersectionPropertyWithReadOnlyKeyword */
     protected readonly Foo&Bar $fooBar;
 
+    /* testTypeIntersectionPropertyWithStaticKeyword */
+    static Foo&Bar $obj;
+
     public function paramTypes(
         /* testTypeIntersectionParam1 */
         Foo&Bar $paramA /* testBitwiseAndParamDefaultValue */ = CONSTANT_A & CONSTANT_B,
diff --git a/tests/Core/Tokenizer/TypeIntersectionTest.php b/tests/Core/Tokenizer/TypeIntersectionTest.php
index 4d18485c39..fcfd191acf 100644
--- a/tests/Core/Tokenizer/TypeIntersectionTest.php
+++ b/tests/Core/Tokenizer/TypeIntersectionTest.php
@@ -109,6 +109,7 @@ public function dataTypeIntersection()
             ['/* testTypeIntersectionPropertyPartiallyQualified */'],
             ['/* testTypeIntersectionPropertyFullyQualified */'],
             ['/* testTypeIntersectionPropertyWithReadOnlyKeyword */'],
+            ['/* testTypeIntersectionPropertyWithStaticKeyword */'],
             ['/* testTypeIntersectionParam1 */'],
             ['/* testTypeIntersectionParam2 */'],
             ['/* testTypeIntersectionParam3 */'],