The Eagles have not won a game in 2023 and are just three points above the Premier League relegation places despite sitting in 12th place in the Premier League table.
Palace chairman Steve Parish said: "It is with enormous regret that this difficult decision has been made.
"Ultimately, results in recent months have placed us in a precarious league position and we felt a change is necessary to give us the best chance of retaining Premier League status."
Under-21 boss Paddy McCarthy will take charge of Palace for their Premier League match away to Arsenal on Sunday (19.03.23).
Vieira had been appointed by the London club in the summer of 2021 and was praised for implementing an attacking style of play as Palace finished 12th last term.
However, the team have only taken five points so far this calendar year and are on a run of three straight league defeats.
Palace will take on eight of their relegation rivals in their final 10 league games and the process of finding a new manager is underway.
Parish said: "Patrick's impact since joining us in the summer of 2021 has been significant, and he is held in the highest regard by myself, and all of his colleagues.
"He led the team to a Wembley FA Cup semi-final and respectable 12th-placed finish last season playing some exciting football, which was a challenging and crucial campaign for the club given the changes we made to the squad prior to his arrival.
"Patrick has given his all to the club, and we all thank him and his team for their service."