Crawford was injured in the first period of the Blackhawks' game Sunday against the Florida Panthers and did not travel with his teammates to Dallas.
Antti Raanta replaced Crawford in the 6-2 win against the Panthers and will start Tuesday against the Dallas Stars. Kent Simpson has been recalled from the American Hockey League to serve as the backup. Regular backup Nikolai Khabibulin is out with a lower-body injury.
Quenneville has no reservations about starting the rookie Raanta, who is 3-0-1 with a 2.16 goals-against average.
"Well, he's handled it well. He's been in the net. Game's been on the line, he's been solid for us. Just moving forward, you like his approach, you like his competitiveness," Quenneville said. "He's a battler. It'll be a good test for him as well."