The Leon midfielder, who won the Apertura and Clausura titles in the 2013-14 Liga MX campaign, netted a stunning goal in Mexico's 3-1 win over Ecuador on Saturday just past the half-hour mark but was carried off the field before half-time.
The 28-year-old, named in Mexico's 23-man squad in early May, lunged into a challenge with Segundo Castillo and both were hurt as their shins collided, with Montes needing several minutes of treatment before he was taken off on a stretcher in clear distress.
A FEMEXFUT statement later confirmed that Montes suffered a broken tibia and fibula as a result of the challenge.
Villarreal midfielder Javier Aquino has been called up in his place, having made 31 La Liga appearances last season.
FEMEXFUT passed on their condolences: "The general director of national teams advises that unfortunately, Luis Montes suffered a broken tibia and fibula in the Mexico match vs. Ecuador, in Dallas, Texas.
"After the game, players, coaching staff and executives of the Mexican team visited the player at the hospital, providing support and solidarity to Luis, who thanked them for their dedication to the Tricolor, and the wishes of a speedy recovery."
Castillo also faces a race against time to make the finals, having sustained a knee injury in the clash.
The Ecuadorean Football Federation (FEF) confirmed after the game that the Al-Hilal player had suffered a hyperextension in his right knee, and he is walking with the aid of crutches as a result.
Further tests will be undertaken on Monday, after which his availability for Brazil is likely to be discovered.
