The car went off the road and plunged down a 60-foot canyon and fell into the river Friday afternoon.
The driver, Evelyn M. Maestas, 60, of Mancos, Colo., and her adopted daughter, Tori, 11, were able to escape through a broken window and get out of the river, highway officials said. They told authorities they saw Maestas' granddaughter, 5-year-old Danica, still inside the Nissan as it sank.
The search was suspended at sundown Saturday. State Trooper Todd Johnson said authorities would determine how to proceed Sunday morning.
Crews were walking along the shore and using the sonar technology, which provides underwater images of the river bottom, but the bottom of the murky water is strewn with large boulders, Sgt. Jeff Nigbur, a Utah Highway Patrol spokesman, told The Associated Press.
"We're having a hard time looking through all the nooks and crannies," Nigbur said Saturday. "The Colorado River is also very dirty and you can't see a thing."
He also said crews didn't know if the car sank quickly or had enough air to help it move farther down the river.
Utah Highway Patrol Sgt. Darrel Mecham said Evelyn and Tori Maestas suffered from hypothermia and were taken to the hospital. Their condition was not immediately available Saturday.