The matchup will be made up in Minnesota at a later date.
The arena was evacuated about 45 minutes before the scheduled 9:30 p.m. EST tipoff when a generator malfunction outside the arena sent smoke pouring into the building, according to NBA spokeswoman Sharon Lima.
Mexico City police said in a statement there was a fire in the generator room on the fourth floor of the modern glass-clad arena that opened in 2012.
"What happened was provoked by a short circuit in the room of generators," the statement said in Spanish.
The teams went to their buses, still wearing their practice gear. About 15 minutes after the scheduled start, the Spurs' bus pulled away from the building. The Timberwolves' bus followed soon after.
While the teams were warming up for their regular-season matchup, lights went out in parts of the arena and smoke began coming out of vents in the upper deck. The court quickly became cloudy.
"I thought they were practicing fireworks," Spurs TV analyst Sean Elliott said. "A lot of teams do that before introductions. But then the smoke just kept creeping and it wasn't white smoke. It was like a brown dark smoke and it started taking over the whole court. It was surprising."
Fans had not yet been allowed into the arena for the NBA's first regular-season game in the country since Houston and Dallas played in Mexico City on Dec. 6, 1997, when the evacuation was ordered.
Spurs guard Manu Ginobili said there was a lot of smoke in their locker room.
Standing outside the Timberwolves' bus in shorts and practice shirt, guard Ricky Rubio had no idea what happened.
"They just told us to leave," Rubio said in Spanish.
Both teams were scheduled to travel home right after the game. The Spurs next host the Indiana Pacers on Saturday night.
The Timberwolves, who play the Miami Heat on Saturday night, were coming off a stretch in which they played a franchise-record 18 games before Dec. 1. The postponement gives them a much-needed break.
Coach Rick Adelman was unhappy that his team had to give up a home game in Minnesota. Now, the Timberwolves will likely make up the game after the return of key bench players Chase Budinger (knee) and Ronny Turiaf (elbow).
Adrian Perez, marketing manager for the arena, said fans will be reimbursed.