Lanzini ruptured ligaments in his right knee during a routine training session on Monday and now will officially miss this summer's tournament.
Perez, who is 32, has been capped 23 times and scored one goal for Argentina. He played for his country at the 2014 FIFA World Cup in Brazil where the team finished runners-up.
Russia will host its first-ever FIFA World Cup from June 14 to July 15, the matches will take place at 12 stadiums in 11 cities across the country. Two-time World Cup winners Argentina will play Iceland, Croatia and Nigeria in Group D at the tournament.