Palace have endured a wretched run of form, which has seen them fail to win in their last 12 matches across all competitions.
A run of three straight defeats in the Premier League has Palace drawing ever closer to the relegation candidates.
A 1-0 loss to Brighton and Hove Albion on Wednesday means Palace are just three points above the relegation zone, though they are in 12th position.
Vieira was appointed Crystal Palace manager in the summer of 2021 after Roy Hodgson's departure and led the Eagles to 12th position in his first full season in charge.
Palace chairman Steve Parish said in a statement: "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.
"That 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."
Vieira, who won the 1998 FIFA World Cup and European Championship in 2000 with France, was captain of the ‘Invincibles’ Arsenal side who went the entire 2003/2004 Premier League season unbeaten.
