The Red Rose full-back was injured after being tackled in the first half of England's 24-15 Six Nations defeat to Ireland at Twickenham on Saturday, which ensured the men in green walked off with their third Grand Slam.
England coach Eddie Jones admitted after the match that it 'did not look good' and those fears have been confirmed following scans.
His club have given no indication on a possible return date but surgery would mean around six months on the sidelines.
Bath director of rugby Todd Blackadder said: "Anthony has been in superb form this year and we're obviously really disappointed to have lost him at a critical part of the season."
Regardless of whether or not he goes under the surgeon's knife, it would seem likely that Watson will miss England's summer tour to South Africa.