The club have won just one of their past seven Premier League matches and are seventh in the table, 12 points behind leaders Chelsea.
First-team coach Michael Carrick has been placed in temporary charge while United seek an interim manager to the end of the season.
"It is with regret that we have reached this difficult decision," United said.
The club's recent run of poor form includes a 5-0 thrashing by Liverpool on 24 October and a 2-0 defeat by Manchester City on 6 November.
United added: "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."
Solskjaer is a former Red Devils player, scoring 126 goals in 11 seasons from 1996-2007 including the winner in the 1999 Champions League final.
United said in their statement: "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."
United next play when they travel to Spain to take on Villarreal in the Champions League on Tuesday, before league games against Chelsea and Arsenal.
Darren Fletcher will stay on as technical director, while Mike Phelan and Kieran McKenna - who were part of Solskjaer's coaching set up - will also remain at the club for the time being.
Former Real Madrid manager Zinedine Zidane, currently out of work, is an early favourite with bookmakers to become United's next manager.