Zhukov's presidency coincided with a turbulent time for Russian sport as a doping scandal led to the country being banned from February's Winter Olympics in South Korea, with some Russian athletes able to compete only under a neutral flag.
"In the current complicated situation in international sport it is very important that the head of the Russian Olympic Committee (ROC) can work in the ROC full-time," Zhukov, who is also a lawmaker in Russia's lower house of parliament, was cited as saying.
"I am unable to do that at the moment due to my heavy workload in parliament," the 61-year-old, who has led the Russian Olympic Committee since 2010, reportedly added.
Allegations that Russia carried out a widespread doping cover-up scheme at the 2014 Sochi Winter Olympics led to suspensions from subsequent Games and a string of investigations by the International Olympic Committee (IOC) and the World Anti-Doping Agency (WADA).
Russian authorities acknowledged transgressions have taken place but have repeatedly denied the existence of a systematic state-sponsored doping programme.
(Writing by Polina Ivanova; Editing by Christian Radnedge)