Former Turkmenistan coach Berdyev, 61, took charge at Rubin in August 2001 and led them to two Russian league titles - the Russian Cup last year and two domestic Supercups - becoming the most successful coach in the club's history.
However, the Kazan-based side are currently languishing at 11th in the league standings with 24 points from 19 games, 16 points behind leaders Zenit St Petersburg. Rubin won only five league matches this season.
Rubin will play Spain's Real Betis in the Europa League round of 32 in February.
(Writing by Angel Krasimirov; editing by Sudipto Ganguly)
