diff --git a/compiler/rustc_ty_utils/src/instance.rs b/compiler/rustc_ty_utils/src/instance.rs
index c50a490a9dc0c..cc4f69744e57f 100644
--- a/compiler/rustc_ty_utils/src/instance.rs
+++ b/compiler/rustc_ty_utils/src/instance.rs
@@ -7,7 +7,7 @@ use rustc_middle::query::Providers;
 use rustc_middle::traits::{BuiltinImplSource, CodegenObligationError};
 use rustc_middle::ty::util::AsyncDropGlueMorphology;
 use rustc_middle::ty::GenericArgsRef;
-use rustc_middle::ty::{self, Instance, TyCtxt, TypeVisitableExt};
+use rustc_middle::ty::{self, Instance, TyCtxt, TypeFlags, TypeVisitableExt};
 use rustc_span::sym;
 use rustc_trait_selection::traits;
 use rustc_type_ir::ClosureKind;
@@ -53,6 +53,15 @@ fn resolve_instance<'tcx>(
                     _ => return Ok(None),
                 }
 
+                // FIXME(#127030): `ConstParamHasTy` has bad interactions with
+                // the drop shim builder, which does not evaluate predicates in
+                // the correct param-env for types being dropped. Stall resolving
+                // the MIR for this instance until all of its const params are
+                // substituted.
+                if ty.has_type_flags(TypeFlags::HAS_CT_PARAM) {
+                    return Ok(None);
+                }
+
                 ty::InstanceKind::DropGlue(def_id, Some(ty))
             } else {
                 debug!(" => trivial drop glue");
diff --git a/tests/ui/const-generics/polymorphic-drop-shim.rs b/tests/ui/const-generics/polymorphic-drop-shim.rs
new file mode 100644
index 0000000000000..4ca2e86cff915
--- /dev/null
+++ b/tests/ui/const-generics/polymorphic-drop-shim.rs
@@ -0,0 +1,18 @@
+//@ compile-flags: -Zinline-mir=yes --crate-type=lib
+//@ build-pass
+
+use std::mem::ManuallyDrop;
+
+pub struct Foo<T, const N: usize>([T; N]);
+
+pub struct Dorp {}
+
+impl Drop for Dorp {
+    fn drop(&mut self) {}
+}
+
+#[inline]
+// SAFETY: call this with a valid allocation idk
+pub unsafe fn drop<const M: usize>(x: *mut Foo<Dorp, M>) {
+    std::ptr::drop_in_place(x);
+}