Having arrived with Genoa 17th in the Italian top flight, Vieira won eight and drew nine of his 26 games last season to guide them to safety and a 13th-place finish.
However, his only two wins this campaign have come in the Coppa Italia, with six defeats in nine games – including five in the past six – in Serie A.
“The club would like to thank the coach and his staff for the dedication and professionalism they have shown throughout their work and wishes them all the best for their future careers,” Genoa’s statement read.
During his playing career, midfielder Vieira won three Premier League titles and four FA Cups at Arsenal, as well as silverware with AC Milan, Inter Milan and Manchester City.
He helped France win the 1998 World Cup and Euro 2000.
Vieira retired in 2011 and became the manager of New York City in 2016.
He returned to Europe with Nice and led them to seventh in Ligue 1 in his first season but was sacked in December 2020.
Vieira became Crystal Palace manager in 2021 and guided them to the FA Cup semi-finals.
He was sacked in 2023 after a 12-game winless run, before joining RC Strasbourg as their first appointment following a takeover by BlueCo, the company which owns Chelsea. He left Strasbourg by mutual consent in July 2024.