diff --git a/src/cdk/overlay/position/flexible-connected-position-strategy.spec.ts b/src/cdk/overlay/position/flexible-connected-position-strategy.spec.ts
index 5ec91669aba1..89b2dab4d1ba 100644
--- a/src/cdk/overlay/position/flexible-connected-position-strategy.spec.ts
+++ b/src/cdk/overlay/position/flexible-connected-position-strategy.spec.ts
@@ -2019,6 +2019,65 @@ describe('FlexibleConnectedPositionStrategy', () => {
         document.body.removeChild(veryLargeElement);
       });
 
+    it('should set the maxWidth and maxHeight on the bounding box when exact dimension are ' +
+      'not used', () => {
+        originElement.style.top = '50px';
+        originElement.style.left = '50%';
+        originElement.style.position = 'fixed';
+
+        positionStrategy
+          .withFlexibleDimensions()
+          .withPositions([{
+            overlayX: 'start',
+            overlayY: 'top',
+            originX: 'start',
+            originY: 'bottom'
+          }]);
+
+        attachOverlay({
+          positionStrategy,
+          maxWidth: 250,
+          maxHeight: 300
+        });
+
+        const overlayStyle = overlayRef.overlayElement.style;
+        const boundingBoxStyle = overlayRef.hostElement.style;
+
+        expect(overlayStyle.maxWidth).toBeFalsy();
+        expect(overlayStyle.maxHeight).toBeFalsy();
+        expect(boundingBoxStyle.maxWidth).toBe('250px');
+        expect(boundingBoxStyle.maxHeight).toBe('300px');
+      });
+
+    it('should set the maxWidth and maxHeight on the overlay pane when exact dimensions are used',
+      () => {
+        originElement.style.bottom = '0';
+        originElement.style.left = '50%';
+        originElement.style.position = 'fixed';
+
+        positionStrategy
+          .withFlexibleDimensions()
+          .withPositions([{
+            overlayX: 'start',
+            overlayY: 'top',
+            originX: 'start',
+            originY: 'bottom'
+          }]);
+
+        attachOverlay({
+          positionStrategy,
+          maxWidth: 250,
+          maxHeight: 300
+        });
+
+        const overlayStyle = overlayRef.overlayElement.style;
+        const boundingBoxStyle = overlayRef.hostElement.style;
+
+        expect(overlayStyle.maxWidth).toBe('250px');
+        expect(overlayStyle.maxHeight).toBe('300px');
+        expect(boundingBoxStyle.maxWidth).toBeFalsy();
+        expect(boundingBoxStyle.maxHeight).toBeFalsy();
+      });
 
   });
 
diff --git a/src/cdk/overlay/position/flexible-connected-position-strategy.ts b/src/cdk/overlay/position/flexible-connected-position-strategy.ts
index 36111025d42d..8f748de9a613 100644
--- a/src/cdk/overlay/position/flexible-connected-position-strategy.ts
+++ b/src/cdk/overlay/position/flexible-connected-position-strategy.ts
@@ -791,7 +791,7 @@ export class FlexibleConnectedPositionStrategy implements PositionStrategy {
 
     if (this._hasExactPosition()) {
       styles.top = styles.left = '0';
-      styles.bottom = styles.right = '';
+      styles.bottom = styles.right = styles.maxHeight = styles.maxWidth = '';
       styles.width = styles.height = '100%';
     } else {
       const maxHeight = this._overlayRef.getConfig().maxHeight;
@@ -860,8 +860,11 @@ export class FlexibleConnectedPositionStrategy implements PositionStrategy {
   /** Sets positioning styles to the overlay element. */
   private _setOverlayElementStyles(originPoint: Point, position: ConnectedPosition): void {
     const styles = {} as CSSStyleDeclaration;
+    const hasExactPosition = this._hasExactPosition();
+    const hasFlexibleDimensions = this._hasFlexibleDimensions;
+    const config = this._overlayRef.getConfig();
 
-    if (this._hasExactPosition()) {
+    if (hasExactPosition) {
       const scrollPosition = this._viewportRuler.getViewportScrollPosition();
       extendStyles(styles, this._getExactOverlayY(position, originPoint, scrollPosition));
       extendStyles(styles, this._getExactOverlayX(position, originPoint, scrollPosition));
@@ -891,12 +894,22 @@ export class FlexibleConnectedPositionStrategy implements PositionStrategy {
     // If a maxWidth or maxHeight is specified on the overlay, we remove them. We do this because
     // we need these values to both be set to "100%" for the automatic flexible sizing to work.
     // The maxHeight and maxWidth are set on the boundingBox in order to enforce the constraint.
-    if (this._hasFlexibleDimensions && this._overlayRef.getConfig().maxHeight) {
-      styles.maxHeight = '';
+    // Note that this doesn't apply when we have an exact position, in which case we do want to
+    // apply them because they'll be cleared from the bounding box.
+    if (config.maxHeight) {
+      if (hasExactPosition) {
+        styles.maxHeight = coerceCssPixelValue(config.maxHeight);
+      } else if (hasFlexibleDimensions) {
+        styles.maxHeight = '';
+      }
     }
 
-    if (this._hasFlexibleDimensions && this._overlayRef.getConfig().maxWidth) {
-      styles.maxWidth = '';
+    if (config.maxWidth) {
+      if (hasExactPosition) {
+        styles.maxWidth = coerceCssPixelValue(config.maxWidth);
+      } else if (hasFlexibleDimensions) {
+        styles.maxWidth = '';
+      }
     }
 
     extendStyles(this._pane.style, styles);