The American was substituted before the 30-minute mark after defender Jason Geria clipped his heel from behind during the match on Tuesday and flew to Italy the next day.
Milan said that an MRI scan revealed the injury and that Pulisic would be re-evaluated in about 10 days. He is set to miss their home clash against Fiorentina on Sunday.
The injury comes around eight months before the World Cup kicks off in the United States, Canada and Mexico, with Pulisic expected to be the biggest draw for the American fans at home.
He is the joint Serie A top scorer with Bologna's Riccardo Orsolini with four goals.