"Manuel Lanzini suffered, in today's morning training, the rupture of the anterior cruciate ligament of his right knee", the federation wrote in a Twitter message.
The 25-year-old has worked his way into head coach Jorge Sampaoli's plans and scored his first senior worldwide goal against Italy in a 2-0 friendly win at the Etihad in March. Argentina begins their World Cup campaign against Iceland next Saturday.
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The 25-year-old had been knocking on the door of national honours for a while, and he finally broke into the Argentina squad last year, when he made his debut against Brazil in Melbourne.
The West Ham United player has suffered a awful ACL injury and is out of the team.
Argentina has yet to name his replacement. All eyes will now be on Argentina coach Jorge Sampaoli to see who will be replacing Lanzini in the squad.
The seriousness of the injury also means Lanzini is likely to miss the opening games of the 2018-19 Premier League season.