Mutko is to appeal to the Court of Arbitration for Sport (CAS) on Tuesday against the decision by the International Olympic Committee (IOC) to ban him from the Games over allegations of state-sponsored doping.
"For the period of the proceedings I will suspend my work at the Russian Football Union for six months," Mutko was quoted as saying by Russian news agencies.
The IOC said this month it was banning Russia from the 2018 Pyeongchang Winter Olympics after finding evidence of "unprecedented systematic manipulation" of doping procedures..
Russia is hosting next year's soccer World Cup in 11 cities including Moscow, St Petersburg and Sochi.
Mutko also said he was considering resigning as head of the World Cup's organising committee (LOC).
"FIFA understands Mr Mutko's decision which was also taken in the best interest of the World Cup next summer," the global soccer body said in a statement. "FIFA thanks Mr. Mutko for this responsible step and for the work carried out so far for the World Cup."
FIFA added that Mutko's decision "will have no impact on the successful staging of the World Cup next summer, as FIFA, the Russian Government, RFU and the LOC continue their fruitful cooperation on the preparations for the World Cup according to plan."
Mutko sat on FIFA's decision-making Council, previously known as the executive committee, from 2009 until earlier this year when he was barred from standing for re-election.
Mutko's position as a government minister was ruled by FIFA's review committee to be incompatible with FIFA statutes demanding political neutrality from its members.
(Reporting by Gabrielle Tétrault-Farber, additional reporting by Brian Homewood in London, writing by Denis Pinchuk, editing by Ed Osmond/Greg Stutchbury)
