Smith didn't practice on Monday, but was on the ice for the morning skate on Tuesday. Coyotes coach Dave Tippett had said he would be a game-time decision.
Blackhawks center Andrew Shaw collided with Smith in Game 2 and was given a five-minute major penalty and game misconduct.
Smith lay on the ice for several minutes while being treated by Phoenix's training staff, but he finished the game. Shaw was suspended by the NHL on Tuesday for three games.
"It's a blatant hit to the head with no intent to miss the goalie," Tippett said. "It's an exact hit they're trying to take out of the game."
Tippett wouldn't elaborate as to whether something popped up regarding Smith's injury after the game.
"That's inconsequential to what outside our locker room has to know," he said.
The Coyotes won 3-2 in overtime Tuesday night to take a 2-1 series lead. Game 4 is Thursday night at the United Center.
ESPNChicago.com's Jesse Rogers and The Associated Press contributed to this report.