An out-of-competition test found the banned substance Furosemide in the 24-year-old's urine sample that was taken in October.
However, Ajax have released a statement claiming that Onana "unwittingly" took the test after feeling unwell, and they will now appeal the ruling at the Court of Arbitration for Sport.
The Dutch champions added that the goalkeeper had mistakenly taken medication prescribed to his wife, but the club clearly state that he "did not intent to cheat".
Onana has been one of Ajax's key players in recent years and his absence will be a blow to a side currently at the top of the Eredivisie table, seven points clear of rivals PSV Eindhoven.
The former Barcelona graduate has kept nine clean sheets in 20 top-flight matches this campaign and played every minute in the group stages of the Champions League, where Ajax finished third behind Liverpool and Atalanta, dropping down to the Europa League in the process.