United have lost five of their last seven league games, including embarrassing defeats to Leicester City, Liverpool and Manchester City recently.
The Red Devils are already 12 points behind leaders Chelsea, whom they face in their next Premier League outing.
Solskjaer was appointed Manchester United manager in December 2018 on an interim basis following the sacking of Jose Mourinho and a bright start led to him being given the role permanently.
The Norwegian led United to third and second place finishes in the top flight in his two full seasons in charge but could not win a trophy, losing the Europa League final to Villarreal in May.
A club statement said: "Manchester United announces that Ole Gunnar Solskjaer has left his role as manager.
"Ole will always be a legend at Manchester United and it is with regret that we have reached this difficult decision. While the past few weeks have been disappointing, they should not obscure all the work he has done over the past three years to rebuild the foundations for long-term success.
"Ole leaves with our sincerest thanks for his tireless efforts as manager and our very best wishes for the future. His place in the club's history will always be secure, not just for his story as a player, but as a great man and a manager who gave us many great moments. He will forever be welcome back at Old Trafford as part of the Manchester United family."
"Michael Carrick will now take charge of the team for forthcoming games, while the club looks to appoint an interim manager to the end of the season."
