The winger suffered the injury during the Swans' 3-1 defeat to Manchester United at the weekend, but it is not known how much football he will miss.
"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," a Swansea statement read.
Montero had just returned to first team action after coming back from a calf injury.