Vieira was appointed by Palace in July 2021Crystal Palace have sacked manager Patrick Vieira after a 12-match winless run.
Palace have not won a match in 2023 and were beaten 1-0 by Brighton in the Premier League on Wednesday, their third defeat in a row.
They are 12th in the table but are only three points above 18th-placed Bournemouth, who have a game in hand.
"It is with enormous regret that this difficult decision has been made," chairman Steve Parish said.
"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."
Frenchman Vieira was appointed before the start of the 2021-22 season and led the Eagles to a 12th-placed finish, earning praise for an attacking style.
However, this season they have scored just 21 goals in 27 games - only Wolves, Everton and bottom-of-the-table Southampton have fewer.
Before their defeat by Brighton, Palace had gone three consecutive games without a shot on target.
Three members of Vieira's coaching staff - Osian Roberts, Kristian Wilson and Said Aigoun - have also left the club and the process of appointing a new manager is under way.
Just five points separate the Premier League's bottom nine clubs heading into the final months of the season.
Palace travel to leaders Arsenal, Vieira's former club, on Sunday (14:00 GMT).
Their final 10 games of the season will see them face all eight of their relegation rivals.
Parish added: "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."
