The 27-year-old suffered the injury in a fall during Sunday's 3-1 defeat by Manchester United after coming on as a half-time substitute.
Montero was able to finish the game and then flew straight to Ecuador for international duty where an X-ray revealed the damage.
A statement on the Swansea website said: " Having been excused international duty, Montero is currently flying back to Swansea to see a specialist and assess whether he is able to continue playing with a cast."
Montero had only just returned to action for the Premier League strugglers following a month and a half out with a calf injury
Source : PA