После сообщения @Nouman_Hanif я получил решение, которое выглядит неплохо.
map_rounded_corner_overlay.xml:
<?xml version="1.0" encoding="UTF-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android">
<stroke android:width="1dp"
android:color="@color/white" />
<corners android:radius="<your_desired_view_corner_radius>"/>
</shape>
Мой файл карты XML:
<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="match_parent"
android:layout_height="match_parent">
<fragment
android:id="@+id/map"
android:name="com.google.android.gms.maps.SupportMapFragment"
android:layout_margin="1dp"
android:layout_width="match_parent"
android:layout_height="match_parent" />
<ImageView
android:layout_width="match_parent"
android:layout_height="match_parent"
android:src="@drawable/map_rounded_corner_overlay" />
</RelativeLayout>