"I have decided to file the claim in the CAS tomorrow," he said.
"So that our organisations are not disturbed during the legal investigation... I have asked to suspend my duties for up to six months," Mutko told journalists after a meeting of the RFU executive committee.
He said that he will continue his duties in the government as well as preparing the World Cup which is being staged in Russia this summer until Russian leadership decides otherwise.
He said he would "suggest" stepping down as chairman of the World Cup organising committee he heads, but "it would be decided by the head of state, the head of government and the supervisory board."
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Mutko said RFU's director Alexander Alayev will become acting president for the duration of his own suspension, which could last less than six months depending on the duration of the legal proceedings.
Mutko said he decided to contest his ban in court because failure to do so would make him seem guilty. However, he denied that he is resigning.
"I'm not resigning, my mandate is still active."
The deputy prime minister had been banned from the Rio 2016 Games. This month he was banned for life from all Olympic Games after the International Olympic Committee said he was involved in a state-backed doping programme.
- FIFA 'understands' decision -
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Despite the ban, Mutko has retained his role as head of the Russia 2018 World Cup organising committee.
FIFA said Monday that Mutko's decision will not impact the World Cup.
"FIFA understands Mr Mutko's decision which was also taken in the best interest of the World Cup next summer. FIFA thanks Mr. Mutko for this responsible step and for the work carried out so far for the World Cup," said a FIFA spokesman.
"Mr 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 local organising committee continue their fruitful cooperation on the preparations for the World Cup according to plan."
Mutko maintained Russian athletes at the 2014 Sochi Olympic Games were clean and that Russia "did a colossal job" to meet requirements by the world anti-doping body to clear its name.
Mutko in March was barred from sitting on the FIFA Council, the world body's ruling top table where the Russian sports official had a seat since 2009.
His participation was blocked because of potential conflicts of interest with his government role.
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