diff --git a/compiler/rustc_borrowck/src/diagnostics/region_name.rs b/compiler/rustc_borrowck/src/diagnostics/region_name.rs
index 517f9e88cd9bd..42662411e4f04 100644
--- a/compiler/rustc_borrowck/src/diagnostics/region_name.rs
+++ b/compiler/rustc_borrowck/src/diagnostics/region_name.rs
@@ -331,7 +331,12 @@ impl<'tcx> MirBorrowckCtxt<'_, '_, 'tcx> {
 
                     let closure_kind = match def_ty {
                         DefiningTy::Closure(_, args) => args.as_closure().kind(),
-                        DefiningTy::CoroutineClosure(_, args) => args.as_coroutine_closure().kind(),
+                        DefiningTy::CoroutineClosure(_, args) => {
+                            match args.as_coroutine_closure().kind() {
+                                ty::ClosureKind::Fn => ty::ClosureKind::FnOnce,
+                                kind => kind,
+                            }
+                        }
                         _ => {
                             // Can't have BrEnv in functions, constants or coroutines.
                             bug!("BrEnv outside of closure.");
@@ -353,7 +358,8 @@ impl<'tcx> MirBorrowckCtxt<'_, '_, 'tcx> {
                              can't escape the closure"
                         }
                         ty::ClosureKind::FnOnce => {
-                            bug!("BrEnv in a `FnOnce` closure");
+                            "closure implements `FnOnce`, so references to captured variables \
+                             can't escape the closure"
                         }
                     };
 
diff --git a/tests/ui/async-await/async-closures/not-lending.stderr b/tests/ui/async-await/async-closures/not-lending.stderr
index f0028129caa02..26c0cab4304c2 100644
--- a/tests/ui/async-await/async-closures/not-lending.stderr
+++ b/tests/ui/async-await/async-closures/not-lending.stderr
@@ -7,7 +7,7 @@ LL |         let x = async move || -> &String { &s };
    |                 |                return type of async closure `{async closure body@$DIR/not-lending.rs:12:42: 12:48}` contains a lifetime `'2`
    |                 lifetime `'1` represents this closure's body
    |
-   = note: closure implements `Fn`, so references to captured variables can't escape the closure
+   = note: closure implements `FnOnce`, so references to captured variables can't escape the closure
 
 error: lifetime may not live long enough
   --> $DIR/not-lending.rs:16:31
@@ -18,7 +18,7 @@ LL |         let x = async move || { &s };
    |                 |           return type of async closure `{async closure body@$DIR/not-lending.rs:16:31: 16:37}` contains a lifetime `'2`
    |                 lifetime `'1` represents this closure's body
    |
-   = note: closure implements `Fn`, so references to captured variables can't escape the closure
+   = note: closure implements `FnOnce`, so references to captured variables can't escape the closure
 
 error: aborting due to 2 previous errors