diff --git a/base/reflection.jl b/base/reflection.jl
index f4a5ca4c7c4b6..ebbca5c178661 100644
--- a/base/reflection.jl
+++ b/base/reflection.jl
@@ -675,12 +675,17 @@ struct type with no fields.
 issingletontype(@nospecialize(t)) = (@_pure_meta; isa(t, DataType) && isdefined(t, :instance))
 
 """
-    typeintersect(T, S)
+    typeintersect(T::Type, S::Type)
 
 Compute a type that contains the intersection of `T` and `S`. Usually this will be the
 smallest such type or one close to it.
 """
-typeintersect(@nospecialize(a), @nospecialize(b)) = (@_pure_meta; ccall(:jl_type_intersection, Any, (Any, Any), a, b))
+function typeintersect(@nospecialize(a), @nospecialize(b))
+    @_pure_meta
+    isa(a, Type) || throw(TypeError(:typeintersect, Type, typeof(a)))
+    isa(b, Type) || throw(TypeError(:typeintersect, Type, typeof(b)))
+    return ccall(:jl_type_intersection, Any, (Any, Any), a, b)
+end
 
 morespecific(@nospecialize(a), @nospecialize(b)) = ccall(:jl_type_morespecific, Cint, (Any, Any), a, b) != 0
 
diff --git a/src/subtype.c b/src/subtype.c
index eb668645552d7..c43d307e6d421 100644
--- a/src/subtype.c
+++ b/src/subtype.c
@@ -1258,7 +1258,6 @@ static int subtype(jl_value_t *x, jl_value_t *y, jl_stenv_t *e, int param)
     }
     if (jl_is_unionall(y))
         return subtype_unionall(x, (jl_unionall_t*)y, e, 1, param);
-    assert(!jl_is_vararg(x) && !jl_is_vararg(y));
     if (jl_is_datatype(x) && jl_is_datatype(y)) {
         if (x == y) return 1;
         if (y == (jl_value_t*)jl_any_type) return 1;
@@ -3107,7 +3106,6 @@ static jl_value_t *intersect(jl_value_t *x, jl_value_t *y, jl_stenv_t *e, int pa
     }
     if (jl_is_unionall(y))
         return intersect_unionall(x, (jl_unionall_t*)y, e, 1, param);
-    assert(!jl_is_vararg(x) && !jl_is_vararg(y));
     if (jl_is_datatype(x) && jl_is_datatype(y)) {
         jl_datatype_t *xd = (jl_datatype_t*)x, *yd = (jl_datatype_t*)y;
         if (param < 2) {
diff --git a/test/subtype.jl b/test/subtype.jl
index 3eca685aee84c..1372abed70a86 100644
--- a/test/subtype.jl
+++ b/test/subtype.jl
@@ -1976,3 +1976,9 @@ end
 @testintersect(Tuple{Type{Pair{_A, S} where S<:AbstractArray{<:_A, 2}}, Dict} where _A,
                Tuple{Type{Pair{_A, S} where S<:AbstractArray{<:_A, 2}} where _A, Union{Array, Pair}},
                Bottom)
+
+# https://github.com/JuliaLang/julia/issues/44735
+@test_throws TypeError(:typeintersect, Type, Core.TypeofVararg) typeintersect(Vararg{Int}, Int)
+@test_throws TypeError(:typeintersect, Type, Core.TypeofVararg) typeintersect(Int, Vararg{Int})
+@test_throws TypeError(:typeintersect, Type, Int) typeintersect(1, Int)
+@test_throws TypeError(:typeintersect, Type, Int) typeintersect(Int, 1)