Blue Cross Blue Shield of Massachusetts has started sending letters to about 55,000 employers and other customers notifying them that Tufts Medical Center and its doctors group is ending its contract with the state’s largest health insurer, effective Jan. 17.

If the contract is terminated, about 88,000 Blue Cross members who have Tufts-affiliated primary care physicians would have to change their doctors by mid-February and the insurer would no longer cover its members’ visits to Tufts. About 157,000 Blue Cross members have had at least two medical claims at the downtown Boston hospital.