diff --git a/src/sage/monoids/free_abelian_monoid.py b/src/sage/monoids/free_abelian_monoid.py
index 590a20eaa1a..ee5e8df0257 100644
--- a/src/sage/monoids/free_abelian_monoid.py
+++ b/src/sage/monoids/free_abelian_monoid.py
@@ -169,6 +169,10 @@ def is_FreeAbelianMonoid(x):
 
         sage: from sage.monoids.free_abelian_monoid import is_FreeAbelianMonoid
         sage: is_FreeAbelianMonoid(5)
+        doctest:warning...
+        DeprecationWarning: the function is_FreeAbelianMonoid is deprecated;
+        use 'isinstance(..., FreeAbelianMonoid_class)' instead
+        See https://github.com/sagemath/sage/issues/37897 for details.
         False
         sage: is_FreeAbelianMonoid(FreeAbelianMonoid(7,'a'))
         True
@@ -177,6 +181,8 @@ def is_FreeAbelianMonoid(x):
         sage: is_FreeAbelianMonoid(FreeMonoid(0,''))
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(37897, "the function is_FreeAbelianMonoid is deprecated; use 'isinstance(..., FreeAbelianMonoid_class)' instead")
     return isinstance(x, FreeAbelianMonoid_class)
 
 
diff --git a/src/sage/monoids/free_monoid.py b/src/sage/monoids/free_monoid.py
index 88277320a63..3e8ed837cf8 100644
--- a/src/sage/monoids/free_monoid.py
+++ b/src/sage/monoids/free_monoid.py
@@ -44,6 +44,10 @@ def is_FreeMonoid(x):
 
         sage: from sage.monoids.free_monoid import is_FreeMonoid
         sage: is_FreeMonoid(5)
+        doctest:warning...
+        DeprecationWarning: the function is_FreeMonoid is deprecated;
+        use 'isinstance(..., (FreeMonoid, IndexedFreeMonoid))' instead
+        See https://github.com/sagemath/sage/issues/37897 for details.
         False
         sage: is_FreeMonoid(FreeMonoid(7,'a'))
         True
@@ -56,6 +60,8 @@ def is_FreeMonoid(x):
         sage: is_FreeMonoid(FreeAbelianMonoid(index_set=ZZ))
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(37897, "the function is_FreeMonoid is deprecated; use 'isinstance(..., (FreeMonoid, IndexedFreeMonoid))' instead")
     if isinstance(x, FreeMonoid):
         return True
     from sage.monoids.indexed_free_monoid import IndexedFreeMonoid
diff --git a/src/sage/monoids/monoid.py b/src/sage/monoids/monoid.py
index 97c0dfa6ad3..c0330ad0eb3 100644
--- a/src/sage/monoids/monoid.py
+++ b/src/sage/monoids/monoid.py
@@ -14,6 +14,10 @@ def is_Monoid(x) -> bool:
 
         sage: from sage.monoids.monoid import is_Monoid
         sage: is_Monoid(0)
+        doctest:warning...
+        DeprecationWarning: the function is_Monoid is deprecated;
+        use 'isinstance(..., Monoid_class)' instead
+        See https://github.com/sagemath/sage/issues/37897 for details.
         False
         sage: is_Monoid(ZZ)   # The technical math meaning of monoid has
         ....:                 # no bearing whatsoever on the result: it's
@@ -26,6 +30,8 @@ def is_Monoid(x) -> bool:
         sage: is_Monoid(F)
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(37897, "the function is_Monoid is deprecated; use 'isinstance(..., Monoid_class)' instead")
     return isinstance(x, Monoid_class)