The 36-year-old was suspended by the International Cricket Council on Tuesday following a series of independent tests.
Concerns over Ajmal's bowling action grew when he was reported to the ICC after his team's first Test match against Sri Lanka in Galle last month.
However, the PCB now hopes to overturn the punishment that was handed out by world cricket's governing body.
"The ban on Ajmal is a big blow to Pakistan cricket and we will appeal against the decision," PCB chairman Shaharyar Khan said in an official statement. "We don't know the exact details but Saeed has the option of also working on his action and taking fresh tests when he is ready.
"What we know is that the ICC has recently changed its protocol on testing bowlers with suspect actions and other bowlers have also been reported. We could appeal in two weeks' time."
Ajmal has taken a total of 446 wickets for Pakistan in all forms of the international game.