The 23-year-old suffered the injury and had to be substituted during Chile's 3-1 friendly defeat to Serbia in Switzerland on Wednesday.
Sanchez, who has only scored once in 15 appearances for Barca this season, will miss a rush of league, Champions League and Copa del Rey games in the run up to Spain's winter break next month.
Coach Tito Vilanova has plenty of cover at present, however.
David Villa and Pedro both scored for Spain in their 5-1 friendly rout of Panama on Wednesday, and winger Cristian Tello has just returned from injury and netted in the win away to Real Mallorca last weekend.
Barca will be seeking to maintain their unbeaten start to La Liga when Real Zaragoza visit on Saturday.