Former player Michael Carrick, a member of Solskjaer's coaching staff, will take charge of the team for Tuesday's Champions League match away to Villarreal with the club saying they will then look to appoint an interim manager to lead the side until the end of the season.
Norwegian Solskjaer had signed a three-year contract extension until 2024 in July but he was dismissed after United lost five of their last seven league games, including defeats by Aston Villa, Leicester City, Liverpool and Manchester City.
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"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," United said in a statement.
"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."
United have not won the Premier League since Alex Ferguson's last season in charge in 2013 when he led them to the title for the 13th time in his reign at Old Trafford.
The club signed Portuguese forward Cristiano Ronaldo in August but after a good start to the campaign they have slipped to seventh in the standings after 12 games, 12 points behind leaders Chelsea.
Solskjaer took over from Jose Mourinho in December, 2018, initially on an interim basis, but after guiding United to 14 wins in 19 matches in all competitions he was given the job permanently in March 2019.
United showed signs of progress to finish third and second in the league in Solskjaer's first full seasons in charge but their form has imploded in this campaign.
The club's hierarchy, including owner Joel Glazer and outgoing executive vice-chairman Ed Woodward, have long faced opposition from fans and the unusual decision to make Carrick a "pre-interim" manager will raise eyebrows.
It is standard practice for clubs to place a member of the coaching staff in temporary charge while they search for a new permanent boss but not for a club to announce they are looking for an interim short-term manager as their next appointment.
Bookmakers have installed former Real Madrid coach and France midfielder Zinedine Zidane as favourite to be the next permanent manager of the club.