Liverpool forward Suarez hit the headlines for all the wrong reasons as Uruguay and Italy battled it out for second spot in Group D on Tuesday.
The South Americans ultimately won 1-0, but the match will not be remembered for the scoreline after Suarez appeared to bite the shoulder of Italian defender Giorgio Chiellini late in the second half.
Suarez has been in trouble before, as he bit PSV Eindhoven's Otman Bakkal in 2010 and was banned for sinking his teeth into the arm of Chelsea's Branislav Ivanovic in 2013.
If found guilty of the offence again, Zyryanov believes FIFA must suspend Suarez from the game, although he feels the forward's case should be dealt with after the World Cup.
"I would allow him to play the rest of the World Cup," he told Sport-Express. "But then he must be punished.
"He already has previous with this, with Branislav Ivanovic who he bit and got a ban for 10 matches.
"They say outside the pitch Suarez is fine, but in the heat of the match his emotions go wild.
"God has shown me mercy (for never being bitten). I've been pushed, beaten off my feet, but biting? Thank God, that has not yet come to anyone's mind."
Russia must beat Algeria in their final Group H match on Thursday in order to qualify for the knockout phase and Zyryanov, who starred for his country at Euro 2008 and Euro 2012, is certain that they will progress and then meet the United States rather than Germany - who face off for top spot in Group G on the same day.
"Of course (Russia will go through)," he added. "I have no doubt. And there is a feeling that in the second round we will get Germany, as everyone is convinced.
"(But) the United States is in their group, which (I think) will occupy the first place. They have a decent team."
