Vieira has overseen a simply torrid run of form, with Palace claiming just one victory in their last 14 Premier League matches, while also being the only winless side in 2023. Their last league win came on December 31st, a 2-0 win at Bournemouth.
This has left them in a precarious position - just three points above the relegation zone.
"It is with enormous regret that this difficult decision has been made," Palace Chairman Steve Parish said.
"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."
Numerous reports in England stated over the last few days that Vieira had one more game to save his job, with the former Arsenal midfielder taking his side to the Emirates this Sunday before the international break.
However, Palace have decided to bite the bullet, and will look to appoint a new man at the helm as soon as possible, with the threat of relegation looming large.
Former France international Vieira, who captained Arsenal to three league titles and four FA Cups as a player, took over from Roy Hodgson in July 2021 on a three-year contract.
He guided Palace to a 12th-placed finish and an FA Cup semi-final run in his first season in charge, and received praise for improving their style of football.
However, they have struggled for goals this season and scored only 21 times in 27 games. Wednesday's defeat at Brighton was their third in a row and marked the 13th league game they failed to score.
"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," Parish added.
"Patrick has given his all to the club, and we all thank him and his team for their service."
Vieira also won the 1998 World Cup and the 2000 European Championship as a player with France. He coached U.S. side New York City FC from 2016-18 before a 2-1/2 year stint at Ligue 1 club Nice.
Three members of his coaching staff, Osian Roberts, Kristian Wilson and Said Aigoun, have also left Palace.
