Lavanini picked up the injury in Argentina's 26-24 victory over South Africa in Salta on Saturday and was not included in the tour party for the Pumas' Oceania leg of the championship when they face New Zealand and Australia.
"Unfortunately, we have just confirmed Tomas Lavanini's injury," team doctor Guillermo Botto said.
"It's a cruciate ligament injury and we expect to do surgery in three to four weeks and then he'll have an estimated recovery time of six months."
The tour squad, posted on the Argentine Rugby Union website (www.uar.com.ar) on Monday, is also missing wing Manuel Montero, who tore a thigh muscle against the Springboks.
Coming into coach Daniel Hourcade's 28-man squad is No 8 Leonardo Senatore, who has served a 10-week suspension for biting handed out during the Super Rugby competition in May.
Matias Moroni returns from the Pumas Olympic rugby sevens team and fellow centre Jeronimo de la Fuente, who also missed Argentina's two matches against the Springboks, is included after recovering from injury.
Felipe Ezcurra was named as a third scrumhalf.
