Suková was a singles runner-up at the Australian Open twice (in 1984 and 1989) and at the US Open twice (in 1986 and 1993).
Njen brat, Cyril Suk III, pa je profesionalni tenisač, s katerim je Suková trikrat zmagala na treh turnirjih za Grand Slam v mešanih dvojicah: na odprtem prvenstvu Francije (1991) in na Wimbledonu (1996, 1997).