The Eagles are just three points above the relegation zone having lost to rivals Brighton on Wednesday evening and are yet to register a victory in 2023.
“It is with enormous regret that this difficult decision has been made,” Palace 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.
“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.”
Three members of Vieira’s coaching staff – Osian Roberts, Kristian Wilson and Said Aigoun – have also left Selhurst Park.
Parish added: “Patrick has given his all to the club, and we all thank him and his team for their service.
“We also wish Patrick, Osian, Kristian and Said the very best for their futures.”
Palace say the process to appoint a new manager is under way and they will provide an update in due course. Dean Kiely will remain as goalkeeping coach.
Palace will next be in action on Sunday when they travel to Arsenal, the Premier League leaders and Vieira’s former club.