Dr. Michelle Carlson in the Hospital for Special Surgery in New York will perform the process a week, sources said.
Robinson, 22, suffered the injury in a triumph over Washington on Friday night.
In his absence, Knicks coach Tom Thibodeau stated Nerlens Noel and Taj Gibson will mostly play the middle position. Julius Randle and newcomer Obi Toppin may also give New York moments there also, Thibodeau said.
After Noel began from the preseason, Thibodeau forced Robinson the starter to start the season, beginning him all 27 matches up to now.
The Knicks have an alternative on Robinson's contract to its 2021-2022 year they can work out, keeping him under contract for $1.8 million, that would leave him an unrestricted free agent following the 2021-22 season.