The CAS said Wednesday the players want to annul their suspensions for failing three times to report their whereabouts for unannounced drug-testing.
The tribunal will issue a ruling within four months.
Wickmayer claims she was not properly informed of the online reporting requirements for drug-testing that led to her ban.
The 20-year-old U.S. Open semifinalist was suspended by a Belgian anti-doping tribunal this month for failing three times to report her whereabouts for drug testing. The ban was confirmed by the International Tennis Federation.
Malisse, a 2002 Wimbledon semifinalist, also was banned a year for the same offense.
Under the World Anti-Doping Agency's rules, elite athletes must be available for out-of-competition testing for one hour a day, 365 days a year. They must give three months' notice of where they will be so they can be tested.