Суарес Наваро е обвързана с приятелката си, Марта.<ref>{{cite web|url=https://womenstennisblog.com/2019/12/02/carla-suarez-navarro-publicizes-love-with-girlfriend/|title=Carla Suarez Navarro publicizes love with girlfriend Marta: “How nice are moments with you”|authour=Marija|work=womenstennisblog.com|date=2 декември 2019|accessdate=15 февруари 2021}} {{Webarchive|url=https://web.archive.org/web/20201127025317/https://womenstennisblog.com/2019/12/02/carla-suarez-navarro-publicizes-love-with-girlfriend/ |date=2020-11-27 }}</ref>
