Mass. Gen. Laws ch. 43 § 26
Except as otherwise provided in sections fifty A, fifty-nine A, eighty-six, one hundred and two and one hundred and twenty-one, if a vacancy occurs in the office of the mayor or city council before the last six months of the term of office, the city council shall order an election for a mayor or a member of the council to serve for the unexpired term; and if such vacancy occurs in the office of mayor in the last six months of the term, the president of the city council shall succeed to said office for the unexpired term. If the mayor is absent or unable from any cause temporarily to perform his duties they shall be performed by the president of the city council. The person upon whom such duties shall devolve shall be called "acting mayor", and he shall possess the powers of mayor only in matters not admitting of delay, but shall have no power to make permanent appointments.
Whenever, under Plan C, any councillor shall be temporarily unable for any cause to perform the duties of his office, the council may appoint one of its members to exercise his powers and perform his duties during such disability. Should an appointive officer of the city be temporarily unable for any cause to perform his duties, the council or the mayor, having the power of original appointment, may make a temporary appointment of some person to act until such official resumes his duties.
Mass. Gen. Laws ch. 43, § 26