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The former Argentina international, who played for clubs including Manchester United, Real Madrid and Paris Saint-Germain, was unable to convert his top-level experience into success on the touchline in the MLS.
Heinze departs after his team won just two of their opening 13 games in the regular season, losing four and drawing seven times to sit 10th in the 14-team Eastern Conference.
A 1-0 defeat to New England on Sunday (AEST) sealed Heinze's fate.
He was appointed in December 2020, and a recent stand-off between the coach and star player Josef Martinez, a former MLS Cup MVP, went down badly with supporters.