Jones, who starred for Ireland 'A' in last summer's Churchill Cup success, damaged neck ligaments as a result of an accidental collision early in the league derby on December 26.
Commenting on the setback for the 22-year-old, Payne said: "Felix is very happy about the treatment he received for the injury and we are looking forward to having him back for the start of next season.
"Of course, we are very disappointed to lose him and all the more so that his injury came at a time when he was playing very well. We are very disappointed for him."
The Dubliner made an encouraging start to his first season with Munster, playing in four successive Magners League games, and he also impressed for Shannon in recent months in the AIB League.
As well as being sidelined for the rest of Munster's Magners League and Heineken Cup campaigns, Jones will miss the Ireland 'A' side's upcoming games against England Saxons (January 31) and Scotland 'A' (February 5).