Torres is said to have sustained the injury during Spain's UEFA Nations League semi-final win against Italy.
But was declared fit for the Nations League final, losing 2-1 to world champions France as he was forced off in the second half.
A statement by Manchester City on the Spaniard's situation read;
"Ferran Torres has suffered an injury to his right foot whilst on international duty," a City statement said on Thursday.
"The City forward, who scored twice in Spain's UEFA Nations League semi-final victory over Italy and also started the showpiece final against France, has picked up a small fracture.
"He has since returned to Manchester for tests and will continue to be monitored."
Torres will miss City's Premier League game with Sean Dyche's Burnley as well as Champions League fixtures against Club Brugge and Paris Saint Germain.
The 21-year-old joined City from Spanish LaLiga club Valencia for a fee believed to be in the region of €23 million.
Torres has made four appearances, scoring 2 goals with one assist in the Premier League.
Torres is still struggling to cement a place in the Manchester City's squad after his arrival from Valencia.
The Citizens currently sit third in the league, two points behind Chelsea.
Pep Guardiola's City are still among the favourites to win the Champions League after losing to Chelsea in the final last season.
