The month-long tournament will be held in 11 cities across the world's largest country - from the Baltic seaport of Kaliningrad to Yekaterinburg, located at the foot of the Ural mountains near the Europe-Asia border, after FIFA dropped two cities from the final list on Saturday.
Mutko, who also heads the local organising committee, said the projected cost is 600 billion roubles (£11.92 billion), which is nearly twice bigger than the original sum, named by then-Prime Minister Vladimir Putin when Russia was awarded the tournament in December 2010.
"These are not the final numbers. You can call these figures a rough estimate," Mutko told a news conference, adding that half of that money would come from the federal government.
Asked when the stadiums would be ready, Mutko said: "We have five arenas (in Moscow, St Petersburg, Kazan, Sochi and Saransk) that are under construction. Next week, I think, we'll start designing four more."
FIFA president Sepp Blatter, who gave Russia "10 out of 10" on Saturday, was again full of praise for the hosts.
"We are one year ahead of schedule. This is a new approach for organising World Cups," Blatter said. "With this approach we have already come so far, six years before the start."
Mutko, however, was more direct in his assessment.
"Today, not one city is ready. Not even Moscow," he said.
Moscow will have two venues - the 90,000-seat Luzhniki stadium which will stage the final and a 45,000-seat arena that is being built by the Spartak club.