The 28-year-old had surgery on Sunday to fix the injury that kept him out of much of Ivory's Coast's triumphant Africa Cup of Nations campaign.
Magpies head coach John Carver said: "He's in Qatar and will stay there for a bit of recovery and then come back."
Asked if that could mean the end of his season, Carver replied: "I would have thought so, yes."
This season Tiote claimed he was injured and unable to play in the first team ... but he managed to play for his country.
His season has played only 12 matches for Newcastle.