diff --git a/compiler/rustc_resolve/src/late/diagnostics.rs b/compiler/rustc_resolve/src/late/diagnostics.rs
index ced272e474d11..521ea7ad184f9 100644
--- a/compiler/rustc_resolve/src/late/diagnostics.rs
+++ b/compiler/rustc_resolve/src/late/diagnostics.rs
@@ -16,6 +16,7 @@ use rustc_hir::def::{self, CtorKind, DefKind};
 use rustc_hir::def_id::{DefId, CRATE_DEF_INDEX, LOCAL_CRATE};
 use rustc_hir::PrimTy;
 use rustc_session::config::nightly_options;
+use rustc_session::parse::feature_err;
 use rustc_span::hygiene::MacroKind;
 use rustc_span::symbol::{kw, sym, Ident, Symbol};
 use rustc_span::{BytePos, Span, DUMMY_SP};
@@ -1599,4 +1600,32 @@ impl<'tcx> LifetimeContext<'_, 'tcx> {
             _ => {}
         }
     }
+
+    /// Non-static lifetimes are prohibited in anonymous constants under `min_const_generics` so
+    /// this function will emit an error if `min_const_generics` is enabled, the body identified by
+    /// `body_id` is an anonymous constant and `lifetime_ref` is non-static.
+    crate fn maybe_emit_forbidden_non_static_lifetime_error(
+        &self,
+        body_id: hir::BodyId,
+        lifetime_ref: &'tcx hir::Lifetime,
+    ) {
+        let is_anon_const = matches!(
+            self.tcx.def_kind(self.tcx.hir().body_owner_def_id(body_id)),
+            hir::def::DefKind::AnonConst
+        );
+        let is_allowed_lifetime = matches!(
+            lifetime_ref.name,
+            hir::LifetimeName::Implicit | hir::LifetimeName::Static | hir::LifetimeName::Underscore
+        );
+
+        if self.tcx.features().min_const_generics && is_anon_const && !is_allowed_lifetime {
+            feature_err(
+                &self.tcx.sess.parse_sess,
+                sym::const_generics,
+                lifetime_ref.span,
+                "a non-static lifetime is not allowed in a `const`",
+            )
+            .emit();
+        }
+    }
 }
diff --git a/compiler/rustc_resolve/src/late/lifetimes.rs b/compiler/rustc_resolve/src/late/lifetimes.rs
index 31360d474736a..072fb509b192a 100644
--- a/compiler/rustc_resolve/src/late/lifetimes.rs
+++ b/compiler/rustc_resolve/src/late/lifetimes.rs
@@ -1777,6 +1777,10 @@ impl<'a, 'tcx> LifetimeContext<'a, 'tcx> {
         let result = loop {
             match *scope {
                 Scope::Body { id, s } => {
+                    // Non-static lifetimes are prohibited in anonymous constants under
+                    // `min_const_generics`.
+                    self.maybe_emit_forbidden_non_static_lifetime_error(id, lifetime_ref);
+
                     outermost_body = Some(id);
                     scope = s;
                 }
diff --git a/src/test/ui/const-generics/min_const_generics/forbid-non-static-lifetimes.rs b/src/test/ui/const-generics/min_const_generics/forbid-non-static-lifetimes.rs
new file mode 100644
index 0000000000000..02944e2bff2f5
--- /dev/null
+++ b/src/test/ui/const-generics/min_const_generics/forbid-non-static-lifetimes.rs
@@ -0,0 +1,27 @@
+#![feature(min_const_generics)]
+
+// This test checks that non-static lifetimes are prohibited under `min_const_generics`. It
+// currently emits an error with `min_const_generics`. This will ICE under `const_generics`.
+
+fn test<const N: usize>() {}
+
+fn issue_75323_and_74447_1<'a>() -> &'a () {
+    test::<{ let _: &'a (); 3 },>();
+   //~^ ERROR a non-static lifetime is not allowed in a `const`
+    &()
+}
+
+fn issue_75323_and_74447_2() {
+    test::<{ let _: &(); 3 },>();
+}
+
+fn issue_75323_and_74447_3() {
+    test::<{ let _: &'static (); 3 },>();
+}
+
+fn issue_73375<'a>() {
+    [(); (|_: &'a u8| (), 0).1];
+    //~^ ERROR a non-static lifetime is not allowed in a `const`
+}
+
+fn main() {}
diff --git a/src/test/ui/const-generics/min_const_generics/forbid-non-static-lifetimes.stderr b/src/test/ui/const-generics/min_const_generics/forbid-non-static-lifetimes.stderr
new file mode 100644
index 0000000000000..cdfd491e39541
--- /dev/null
+++ b/src/test/ui/const-generics/min_const_generics/forbid-non-static-lifetimes.stderr
@@ -0,0 +1,21 @@
+error[E0658]: a non-static lifetime is not allowed in a `const`
+  --> $DIR/forbid-non-static-lifetimes.rs:9:22
+   |
+LL |     test::<{ let _: &'a (); 3 },>();
+   |                      ^^
+   |
+   = note: see issue #44580 <https://github.com/rust-lang/rust/issues/44580> for more information
+   = help: add `#![feature(const_generics)]` to the crate attributes to enable
+
+error[E0658]: a non-static lifetime is not allowed in a `const`
+  --> $DIR/forbid-non-static-lifetimes.rs:23:16
+   |
+LL |     [(); (|_: &'a u8| (), 0).1];
+   |                ^^
+   |
+   = note: see issue #44580 <https://github.com/rust-lang/rust/issues/44580> for more information
+   = help: add `#![feature(const_generics)]` to the crate attributes to enable
+
+error: aborting due to 2 previous errors
+
+For more information about this error, try `rustc --explain E0658`.