diff --git a/compiler/rustc_mir/src/interpret/step.rs b/compiler/rustc_mir/src/interpret/step.rs
index 0f365eaa41d..2bed3b2c3ad 100644
--- a/compiler/rustc_mir/src/interpret/step.rs
+++ b/compiler/rustc_mir/src/interpret/step.rs
@@ -115,11 +115,10 @@ impl<'mir, 'tcx: 'mir, M: Machine<'mir, 'tcx>> InterpCx<'mir, 'tcx, M> {
             }
 
             // Call CopyNonOverlapping
-            CopyNonOverlapping(box rustc_middle::mir::CopyNonOverlapping { dst, src, count }) => {
-                let count = self.eval_operand(count, None)?;
-
+            CopyNonOverlapping(box rustc_middle::mir::CopyNonOverlapping { src, dst, count }) => {
                 let src = self.eval_operand(src, None)?;
                 let dst = self.eval_operand(dst, None)?;
+                let count = self.eval_operand(count, None)?;
                 self.copy(&src, &dst, &count, /* nonoverlapping */ true)?;
             }
 
@@ -160,16 +159,18 @@ impl<'mir, 'tcx: 'mir, M: Machine<'mir, 'tcx>> InterpCx<'mir, 'tcx, M> {
         let count = self.read_scalar(&count)?.to_machine_usize(self)?;
         let layout = self.layout_of(src.layout.ty.builtin_deref(true).unwrap().ty)?;
         let (size, align) = (layout.size, layout.align.abi);
+        let size = size.checked_mul(count, self).ok_or_else(|| {
+            err_ub_format!("overflow computing total size of `copy_nonoverlapping`")
+        })?;
+
+        // Make sure we check both pointers for an access of the total size and aligment,
+        // *even if* the total size is 0.
         let src =
             self.memory.check_ptr_access(self.read_scalar(&src)?.check_init()?, size, align)?;
 
         let dst =
             self.memory.check_ptr_access(self.read_scalar(&dst)?.check_init()?, size, align)?;
 
-        let size = size.checked_mul(count, self).ok_or_else(|| {
-            err_ub_format!("overflow computing total size of `copy_nonoverlapping`")
-        })?;
-
         if let (Some(src), Some(dst)) = (src, dst) {
             self.memory.copy(src, dst, size, nonoverlapping)?;
         }
diff --git a/src/test/ui/consts/copy-intrinsic.rs b/src/test/ui/consts/copy-intrinsic.rs
new file mode 100644
index 00000000000..6b46b9317d0
--- /dev/null
+++ b/src/test/ui/consts/copy-intrinsic.rs
@@ -0,0 +1,31 @@
+// ignore-tidy-linelength
+#![feature(const_mut_refs, const_intrinsic_copy, const_ptr_offset)]
+use std::ptr;
+
+const COPY_ZERO: () = unsafe {
+    // Since we are not copying anything, this should be allowed.
+    let src = ();
+    let mut dst = ();
+    ptr::copy_nonoverlapping(&src as *const _ as *const i32, &mut dst as *mut _ as *mut i32, 0);
+};
+
+const COPY_OOB_1: () = unsafe {
+    let mut x = 0i32;
+    let dangle = (&mut x as *mut i32).wrapping_add(10);
+    // Even if the first ptr is an int ptr and this is a ZST copy, we should detect dangling 2nd ptrs.
+    ptr::copy_nonoverlapping(0x100 as *const i32, dangle, 0); //~ ERROR any use of this value will cause an error
+    //~| memory access failed: pointer must be in-bounds
+    //~| previously accepted
+};
+const COPY_OOB_2: () = unsafe {
+    let x = 0i32;
+    let dangle = (&x as *const i32).wrapping_add(10);
+    // Even if the second ptr is an int ptr and this is a ZST copy, we should detect dangling 1st ptrs.
+    ptr::copy_nonoverlapping(dangle, 0x100 as *mut i32, 0); //~ ERROR any use of this value will cause an error
+    //~| memory access failed: pointer must be in-bounds
+    //~| previously accepted
+};
+
+
+fn main() {
+}
diff --git a/src/test/ui/consts/copy-intrinsic.stderr b/src/test/ui/consts/copy-intrinsic.stderr
new file mode 100644
index 00000000000..9157ba50dde
--- /dev/null
+++ b/src/test/ui/consts/copy-intrinsic.stderr
@@ -0,0 +1,37 @@
+error: any use of this value will cause an error
+  --> $DIR/copy-intrinsic.rs:16:5
+   |
+LL | / const COPY_OOB_1: () = unsafe {
+LL | |     let mut x = 0i32;
+LL | |     let dangle = (&mut x as *mut i32).wrapping_add(10);
+LL | |     // Even if the first ptr is an int ptr and this is a ZST copy, we should detect dangling 2nd ptrs.
+LL | |     ptr::copy_nonoverlapping(0x100 as *const i32, dangle, 0);
+   | |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ memory access failed: pointer must be in-bounds at offset 40, but is outside bounds of alloc4 which has size 4
+LL | |
+LL | |
+LL | | };
+   | |__-
+   |
+   = note: `#[deny(const_err)]` on by default
+   = warning: this was previously accepted by the compiler but is being phased out; it will become a hard error in a future release!
+   = note: for more information, see issue #71800 <https://github.com/rust-lang/rust/issues/71800>
+
+error: any use of this value will cause an error
+  --> $DIR/copy-intrinsic.rs:24:5
+   |
+LL | / const COPY_OOB_2: () = unsafe {
+LL | |     let x = 0i32;
+LL | |     let dangle = (&x as *const i32).wrapping_add(10);
+LL | |     // Even if the second ptr is an int ptr and this is a ZST copy, we should detect dangling 1st ptrs.
+LL | |     ptr::copy_nonoverlapping(dangle, 0x100 as *mut i32, 0);
+   | |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ memory access failed: pointer must be in-bounds at offset 40, but is outside bounds of alloc6 which has size 4
+LL | |
+LL | |
+LL | | };
+   | |__-
+   |
+   = warning: this was previously accepted by the compiler but is being phased out; it will become a hard error in a future release!
+   = note: for more information, see issue #71800 <https://github.com/rust-lang/rust/issues/71800>
+
+error: aborting due to 2 previous errors
+