Wendy Alexander faces increased pressure to step down over a donations scandal.
Tony McElroy, a former press officer for Gordon Brown and Scottish Labour's head of comms for almost five years, will join Tesco as corporate affairs manager for Scotland.
McElroy will move to Tesco in April. He will be the third comms person to leave Scottish Labour since Alexander became leader last year. Senior press officer Brian Lironi left in November and press aide Matthew Marr resigned in disgrace after shouting an obscenity at First Minister Alex Salmond.