The angler waded into the Spanish Fork River around noon and then noticed a car upside-down in the water, public safety officials said in a statement.
Rescuers arrived and tipped the four-door car onto its side. They found the 18-month-old girl strapped in her car seat, still alive. The baby was taken to a Salt Lake City hospital, where she was in critical condition.
Rescuers also found the body of Lynn Jennifer Groesbeck, the girl's mother, in the driver's seat. She was 25 years old.
A resident nearby told authorities that he had heard a loud crash the night before around 10:30 and stepped outside to check, but saw nothing unusual, police said.
If that sound was the car going into the river, then the baby was trapped in the car for about 14 hours.
Police are investigating the incident as a traffic accident, though many questions remain unanswered.
"This is just a tragedy all the way around," Spanish Fork Police Lt. Matt Johnson said. "There's not anything at the scene, as far as evidence goes, as why the vehicle left roadway. There were no skid marks to show evasive maneuvers, to show why the vehicle left the roadway and traveled into the river."
The car was towed and is being examined to determine whether there was brake failure or some other malfunction, Johnson said.
Family members of the mother told police she had left Salem, Utah, and was supposed to be heading to her home in Springville, about 9 miles away.
The baby, who was in a car seat in the rear passenger side, was not submerged during the ordeal, Johnson said.
Three police officers and four firefighters were treated at a hospital for hypothermia. The rescuers have since been released.