Jose Mourihno, the Portuguese, 55, took over in May 2016 and led United to League Cup and Europa League titles but they are 19 points behind league leaders Liverpool.
The club have made a change after no progress with results or style despite spending nearly £400m on 11 players.
The club also says the new manager will understand the philosophy of the club, including its attacking traditions.
It is understood that players and staff are not happy after a disappointing and unsettling period during which young players were not developed.
Manchester United are sixth in the Premier League, but closer to the relegation zone than leaders Liverpool, who beat them 3-1 on Sunday.
The decision to sack Mourinho, which will cost more than £18m, has been taken in the long-term interests of Manchester United with a regard that the club is bigger than any one individual.
Mourinho is understood to have wanted his own structure, but the new manager will be appointed with a head of football above him reporting to executive vice-chairman Ed Woodward.
A United statement said: “A caretaker-manager will be appointed until the end of the season while the club conducts a thorough recruitment process for a new, full-time manager.
“The club would like to thank Jose for his work during his time at Manchester United and to wish him success in the future.”
The club hope to appoint a caretaker-manager before they face Cardiff City on 22 December but it will not be assistant manager Michael Carrick or academy boss Nicky Butt.
The candidate will be drawn from outside the club, but will not be former Arsenal boss Arsene Wenger.
A familiar conclusion to a rocky season
United’s haul of 26 points after their first 17 Premier League games, is their worst tally in the top flight at this stage since 1990-91.
They are 11 points off the top four which would earn a Champions League qualification place.
Mourinho’s sacking comes after a fall-out with £89m record signing Paul Pogba, who was an unused substitute for the defeat at Anfield on Sunday.
Following a 1-1 draw with Wolves, midfielder Pogba said he wanted United to be able to “attack, attack, attack” at home, which led Mourinho to say the France midfielder would no longer be the club’s “second captain”.
After Mourinho, who replaced Louis van Gaal in May 2016 and signed a contract extension in January, was sacked Pogba tweeted: “Caption this,” with a knowing expression on his face, before deleting the social media post.
Former Manchester United defender Gary Neville replied: “You do one as well!”
In October, there were reports that Mourinho might be sacked prior to the home game against Newcastle, but after the team trailed 2-0, they turned it around to win 3-2 and seemingly buy the former Chelsea, Inter Milan and Real Madrid boss more time.
Mourinho’s agent Jorge Mendes attempted to calm the storm earlier in December by taking the extraordinary step of issuing a statement to say Mourinho was “very happy” and “fully committed” to the club.
But despite reaching the Champions League last 16, where United will play Paris St-Germain, they have won just one of their past six games in the Premier League.
Mourinho’s dismissal continues his run of never completing four consecutive seasons in charge of a club.
Only once has he made it into a fourth campaign, but he left Chelsea on 20 September 2007 during his first spell at Stamford Bridge.