The former Newcastle United player was stretchered off during last Saturday's 2-2 draw with Manchester City at the Emirates.
After the match, reports emerged claiming that the Frenchman would be sidelined for two months, but the player himself has now stated that he has a "broken" ankle ligament.
The 29-year-old wrote on his Facebook page: "No fracture but one broken ligament ... I have to wait until Friday in order to know if I must have surgery."
Debuchy signed for the Gunners from Newcastle in the summer.