diff --git a/marshmallow_dataclass/__init__.py b/marshmallow_dataclass/__init__.py
index 7ad8da5..1cde8a6 100644
--- a/marshmallow_dataclass/__init__.py
+++ b/marshmallow_dataclass/__init__.py
@@ -480,19 +480,35 @@ def _field_by_supertype(
         )
 
 
+COLLECTIONS_TYPES: Dict[str, Set[Type]] = {
+    "list": {list, List},
+    "dict": {dict, Dict},
+    "mapping": {Mapping},
+    "sequence": {Sequence},
+    "set": {set, Set},
+    "frozenset": {frozenset, FrozenSet},
+}
+
+if sys.version_info >= (3, 9):
+    # supporting PEP 585 collections types
+    COLLECTIONS_TYPES["mapping"] |= {collections.abc.Mapping}
+    COLLECTIONS_TYPES["sequence"] |= {collections.abc.Sequence}
+    COLLECTIONS_TYPES["set"] |= {collections.abc.Set}
+
+
 def _generic_type_add_any(typ: type) -> type:
     """if typ is generic type without arguments, replace them by Any."""
-    if typ in (list, List):
+    if typ in COLLECTIONS_TYPES["list"]:
         typ = List[Any]
-    elif typ in (dict, Dict):
+    elif typ in COLLECTIONS_TYPES["dict"]:
         typ = Dict[Any, Any]
-    elif typ in (Mapping, collections.abc.Mapping):
+    elif typ in COLLECTIONS_TYPES["mapping"]:
         typ = Mapping[Any, Any]
-    elif typ in (Sequence, collections.abc.Sequence):
+    elif typ in COLLECTIONS_TYPES["sequence"]:
         typ = Sequence[Any]
-    elif typ in (set, Set, collections.abc.Set):
+    elif typ in COLLECTIONS_TYPES["set"]:
         typ = Set[Any]
-    elif typ in (frozenset, FrozenSet):
+    elif typ in COLLECTIONS_TYPES["frozenset"]:
         typ = FrozenSet[Any]
     return typ