Watson, the No. 18 Tigers' star freshman, played with the torn ACL in a 35-17 victory over rival South Carolina on Nov. 29. The coach said then that Watson would be available to play in the Russell Athletic Bowl on Dec. 29 against Oklahoma (8-4).
However, Swinney changed that stance Sunday, saying an operation would give Watson a jump-start on rehab if he had the surgery now.
This will be Watson's second operation this season. He broke a bone in his throwing hand against Louisville in October and missed his next three starts. He returned against Georgia Tech in November, but played less than a quarter before injuring his knee.
Watson missed four games with injuries this fall. He threw for 269 yards and accounted for four TDs in the win over South Carolina.
The Associated Press contributed to this report.