diff --git a/packages/components/src/popover/index.js b/packages/components/src/popover/index.js
index f2051a7d839e7..36b001ae50cbe 100644
--- a/packages/components/src/popover/index.js
+++ b/packages/components/src/popover/index.js
@@ -71,11 +71,17 @@ function computeAnchorRect(
 			return;
 		}
 
-		if ( anchorRef instanceof window.Range ) {
+		// Duck-type to check if `anchorRef` is an instance of Range
+		// `anchorRef instanceof window.Range` checks will break across document boundaries
+		// such as in an iframe
+		if ( typeof anchorRef?.cloneRange === 'function' ) {
 			return getRectangleFromRange( anchorRef );
 		}
 
-		if ( anchorRef instanceof window.Element ) {
+		// Duck-type to check if `anchorRef` is an instance of Element
+		// `anchorRef instanceof window.Element` checks will break across document boundaries
+		// such as in an iframe
+		if ( typeof anchorRef?.getBoundingClientRect === 'function' ) {
 			const rect = anchorRef.getBoundingClientRect();
 
 			if ( shouldAnchorIncludePadding ) {