Torres scored both goals in Spain’s 2-1 win over Italy in the UEFA Nations League semi-finals, but limped in the second half after being kicked in the foot.
The 21-year-old was initially uncertain before coming to his 2-1 loss to France in the final on Sunday.
City did not provide a timeline for Torres’ return and said in a press release he would undergo further tests in Manchester.
Spanish media reported he could be out of action for six weeks.
The city is attacking Burnley in the league on Saturday.