diff --git a/src/test/ui/const-generics/issue-66596-impl-trait-for-str-const-arg.rs b/src/test/ui/const-generics/issue-66596-impl-trait-for-str-const-arg.rs
new file mode 100644
index 0000000000000..b677dcc4af4b4
--- /dev/null
+++ b/src/test/ui/const-generics/issue-66596-impl-trait-for-str-const-arg.rs
@@ -0,0 +1,16 @@
+// check-pass
+
+#![feature(const_generics)]
+//~^ WARN the feature `const_generics` is incomplete and may cause the compiler to crash
+
+trait Trait<const NAME: &'static str> {
+    type Assoc;
+}
+
+impl Trait<"0"> for () {
+    type Assoc = ();
+}
+
+fn main() {
+    let _: <() as Trait<"0">>::Assoc = ();
+}
diff --git a/src/test/ui/const-generics/issue-66596-impl-trait-for-str-const-arg.stderr b/src/test/ui/const-generics/issue-66596-impl-trait-for-str-const-arg.stderr
new file mode 100644
index 0000000000000..8ab28cc2a8580
--- /dev/null
+++ b/src/test/ui/const-generics/issue-66596-impl-trait-for-str-const-arg.stderr
@@ -0,0 +1,8 @@
+warning: the feature `const_generics` is incomplete and may cause the compiler to crash
+  --> $DIR/issue-66596-impl-trait-for-str-const-arg.rs:3:12
+   |
+LL | #![feature(const_generics)]
+   |            ^^^^^^^^^^^^^^
+   |
+   = note: `#[warn(incomplete_features)]` on by default
+