The centre suffered the injury to his left foot during the first half of Bath’s 41-6 defeat to Saracens at Allianz Park last Sunday.
Director of Rugby, Todd Blackadder, said: “JJ is going to need surgery to correct his injury. He will then need a lengthy period of time to rehabilitate.
“Our medical team will work closely with him to ensure we get him back on the pitch as soon as possible.”