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.
