Torres scored both goals in Spain’s 2-1 win over Italy in the UEFA Nations League semifinal, but limped off in the second half after suffering a blow to his foot.
The 21-year-old was initially a doubt before playing in their 2-1 defeat by France in the final on Sunday.
City did not provide a timeline for Torres’s return and said in a statement he would undergo further tests in Manchester.
Spanish media reported that he could be out of action for six weeks.
City take on Burnley in the league on Saturday.