Vasilyev, who joined the principality side as an advisor to president Dmitry Rybolovlev in January 2013, leaves his current post following six successful years on the French Riviera.
"We have achieved much success: the club has finished in the top three of Ligue 1 five times; we won Ligue 1 for the first time in 17 years; and we reached the semifinals of the Champions League," Monaco's statement read.
"However, over the past year, serious mistakes had been made that have led to the team’s worst performance in seven years."
Vasilyev is largely credited with Monaco's recruitment process following the club's return to top-flight football for the 2013-14 season. The Russian businessman orchestrated moves for the likes of Radamel Falcao, Joao Moutinho, and James Rodriguez before shifting his focus to sales.
"I would like to thank President Dmitry Rybolovlev for allowing me to lead AS Monaco and to live this exceptional experience, so rich in emotions. During this time, I did my best to allow the club to obtain results in line with our ambitions," Rybolovlev's statement added.