Vieira who has been in charge of the club for 20 months was relieved of his duties after a 12-match winless run.
Palace has not won a match in 2023 and were beaten 1 nil by Brighton in the Premier League on Wednesday, their third defeat in a row.
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Palace are currently battling relegation and are 12th in the table but are only three points above 18th-placed Bournemouth, who have a game in hand.