The 49-year-old was appointed Cincinnati manager in May last year on a two-year contract but won just eight of his 47 games in charge.
The former Feyenoord manager has also lost six of his last seven games, with Cincinnati second from bottom in the Eastern Conference.
The club released a statement which said: "During our nearly two-month process to identify the next general manager for FC Cincinnati, it was apparent that a head coach change was necessary.
"Therefore, after a great deal of deliberation, the club has made the decision to now move to the future with Jaap no longer serving as head coach."
President Jeff Berding said. "We believe a change in leadership is in the best interest of the club at this time, and a new General Manager will lead the search for a new Head Coach.
"We are an ambitious club and we remain focused on achieving our goals, the first of which is making Cincinnati a championship city.
"We thank Jaap for everything he has done for FC Cincinnati during his time here, and we wish him the best as he can now head home to be with his family."
Stam has previously managed Reading in the second-tier of English football, and nearly took them to Premier League promotion in 2017 but lost out to Huddersfield on penalties in the play-off final.
Stam was part of the Manchester United side that famously won the treble in 1999 while he also had spells at Lazio, AC Milan and Ajax Amsterdam.
