diff --git a/changes/1466-MrMrRobat.md b/changes/1466-MrMrRobat.md
new file mode 100644
index 0000000000..1e1cb3b1cc
--- /dev/null
+++ b/changes/1466-MrMrRobat.md
@@ -0,0 +1 @@
+Make `BaseModel.__signature__` class-only, so getting `__signature__` from model instance will raise `AttributeError`
\ No newline at end of file
diff --git a/pydantic/main.py b/pydantic/main.py
index e1161d7fcd..bb01d2e3cc 100644
--- a/pydantic/main.py
+++ b/pydantic/main.py
@@ -35,6 +35,7 @@
 from .types import PyObject, StrBytes
 from .typing import AnyCallable, AnyType, ForwardRef, is_classvar, resolve_annotations, update_field_forward_refs
 from .utils import (
+    ClassAttribute,
     GetterDict,
     Representation,
     ValueItems,
@@ -300,7 +301,8 @@ def __new__(mcs, name, bases, namespace, **kwargs):  # noqa C901
         }
 
         cls = super().__new__(mcs, name, bases, new_namespace, **kwargs)
-        cls.__signature__ = generate_model_signature(cls.__init__, fields, config)
+        # set __signature__ attr only for model class, but not for its instances
+        cls.__signature__ = ClassAttribute('__signature__', generate_model_signature(cls.__init__, fields, config))
         return cls
 
 
diff --git a/pydantic/utils.py b/pydantic/utils.py
index 1a31192a5e..fdd4f59a07 100644
--- a/pydantic/utils.py
+++ b/pydantic/utils.py
@@ -45,6 +45,7 @@
     'GetterDict',
     'ValueItems',
     'version_info',  # required here to match behaviour in v1.3
+    'ClassAttribute',
 )
 
 
@@ -439,3 +440,23 @@ def _normalize_indexes(
 
     def __repr_args__(self) -> 'ReprArgs':
         return [(None, self._items)]
+
+
+class ClassAttribute:
+    """
+    Hide class attribute from its instances
+    """
+
+    __slots__ = (
+        'name',
+        'value',
+    )
+
+    def __init__(self, name: str, value: Any) -> None:
+        self.name = name
+        self.value = value
+
+    def __get__(self, instance: Any, owner: Type[Any]) -> None:
+        if instance is None:
+            return self.value
+        raise AttributeError(f'{self.name!r} attribute of {owner.__name__!r} is class-only')
diff --git a/tests/test_model_signature.py b/tests/test_model_signature.py
index 6b384a7b15..789372b9b3 100644
--- a/tests/test_model_signature.py
+++ b/tests/test_model_signature.py
@@ -126,3 +126,15 @@ class Config:
             extra = Extra.allow
 
     assert _equals(str(signature(Model)), '(extra_data: int = 1, **foobar: Any) -> None')
+
+
+def test_signature_is_class_only():
+    class Model(BaseModel):
+        foo: int = 123
+
+        def __call__(self, a: int) -> bool:
+            pass
+
+    assert _equals(str(signature(Model)), '(*, foo: int = 123) -> None')
+    assert _equals(str(signature(Model())), '(a: int) -> bool')
+    assert not hasattr(Model(), '__signature__')
diff --git a/tests/test_utils.py b/tests/test_utils.py
index a58e14f688..feb373ce60 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -12,7 +12,15 @@
 from pydantic.dataclasses import dataclass
 from pydantic.fields import Undefined
 from pydantic.typing import display_as_type, is_new_type, new_type_supertype
-from pydantic.utils import ValueItems, deep_update, get_model, import_string, lenient_issubclass, truncate
+from pydantic.utils import (
+    ClassAttribute,
+    ValueItems,
+    deep_update,
+    get_model,
+    import_string,
+    lenient_issubclass,
+    truncate,
+)
 from pydantic.version import version_info
 
 try:
@@ -298,3 +306,17 @@ def test_version_info():
 
 def test_version_strict():
     assert str(StrictVersion(VERSION)) == VERSION
+
+
+def test_class_attribute():
+    class Foo:
+        attr = ClassAttribute('attr', 'foo')
+
+    assert Foo.attr == 'foo'
+
+    with pytest.raises(AttributeError, match="'attr' attribute of 'Foo' is class-only"):
+        Foo().attr
+
+    f = Foo()
+    f.attr = 'not foo'
+    assert f.attr == 'not foo'