Miami seemed poised to dominate their way to the championship after an unprecedented 74-point regular season. However, their dreams were shattered when they suffered a surprising defeat in the best-of-three opening round to the ninth seed Atlanta earlier this month.
Martino, who coached Messi for the Argentina national team and at Barcelona, joined Miami last year.
He is set to appear at a press conference on Friday with Managing Owner Jorge Mas. Media reports cited "personal reasons" as his reason for stepping down.