Kunnas made her international debut for Finland in a 1996 Algarve Cup match against Sweden. After making one appearance per year in 1996, 1997 and 1998, she became Finland's main goalkeeper after Johanna Lindell retired in 2004. That year, she was part of the first Finland team to qualify for the UEFA Women's Championship. Kunnas represented Finland at UEFA Women's Euro 2005, where they finished joint third, after losing their semi-final 4–1 to Germany. She was praised by teammate Laura Kalmari for her performance in Finland's group stage match against Denmark, a match they won 2–1. She retired from international football after UEFA Euro 2005. In total, Kunnas made 46 appearances for Finland.