The Leon midfielder, who won the Apertura and Clausura titles in the 2013-14 Liga MX campaign, netted a stunning goal 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.
Marco Fabian and a Maximo Banguera own goal extended Mexico's lead after the break at a packed AT&T Stadium on Saturday, with substitute Enner Valencia scoring for Ecuador late on.
But it was the injury to Montes, rather than Ecuador's consolation, that will have overshadowed the game for Mexico coach Miguel Herrera, who maintained his unbeaten run at the helm.
There were happier scenes before the game as defender Andres Guardado was presented with a trophy to mark his 100th appearance for his country, the 10th Mexican to achieve the feat.
A series of long-range free-kicks were the only openings to punctuate an otherwise tame first 30 minutes as both sides were guilty of playing loose passes in the final third.
Giovani dos Santos was the first to fire a set-piece over the crossbar in the fourth minute, while Jorge Guagua was also wayward with his 27th-minute effort.
But Montes provided the first moment of genuine quality as he collected Rafael Marquez's pass before arrowing a superb strike past goalkeeper Banguera from 20 yards.
His night turned sour just a few minutes later, though, in a challenge that also led to Castillo being withdrawn from the action.
Montes was guilty of mistiming his tackle and, while he looks almost certain to miss the trip to Brazil if reports of a suspected fracture are confirmed, Castillo may also be a doubt for Reinaldo Rueda's yet-to-be-finalised squad.
Some of Montes' team-mates were visibly upset by the incident and the match was understandably subdued for a while after the interval, with Marquez also having to be taken off with an apparent foot injury.
To their credit, Mexico found their rhythm after a slow start to the second half and, after Paul Aguilar cleared from underneath his own crossbar, they doubled their lead in the 69th minute courtesy of Fabian's dipping effort from well outside the box.
Banguera then made a mess of trying to keep out Dos Santos' tame shot seven minutes later, the ball coming back off the post and going in via the goalkeeper to make it 3-0.
Valencia's deflected free-kick gave Ecuador something to cheer, but there was also plenty to ponder for Rueda with a friendly against England to come before their World Cup campaign begins with a Group E clash against Switzerland on June 15.
Mexico, meanwhile, are likely to need to draft in one of their standby players before next week's friendlies against Bosnia-Herzegovina and Portugal, with group-stage clashes versus Cameroon, Brazil and Croatia to follow.
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