"WADA is seeking a period of ineligibility of between one and two years," it said in a statement after the Italian twice tested positive for the banned substance clostebol in March but was cleared to carry on playing.
Sinner, who recently won the US Open and is currently in action in Beijing, has consistently denied wrongdoing.
Last month, the International Tennis Integrity Agency (ITIA) said that Sinner had been cleared of any wrongdoing after twice testing positive earlier in the season.
The ITIA accepted his explanation that the drug entered his system when his physiotherapist used a spray containing it to treat a cut, then provided massage and sports therapy to the player.
The global anti-doping body said in its statement that it lodged its appeal against the ruling to CAS, the top court in sport, on Thursday.
"It is WADA's view that the finding of 'no fault or negligence' was not correct under the applicable rules," it said.
It added: "WADA is not seeking a disqualification of any results, save that which has already been imposed by the tribunal of first instance.
"As this matter is now pending before CAS, WADA will make no further comment at this time."
Clostebol is an anabolic agent prohibited at all times by WADA.
