The crash was reported at 2:55 p.m. off of U.S. Highway 50 near Kyburz, a town approximately 75 miles east of Sacramento, Sgt. Mike Poore said.
The SUV went off the roadway and struck a concrete mile marker, a tree and a boulder before landing on its side in the river, he said.
Inside the SUV there was a mother, father and three daughters -- twin 13-year-olds and a 4-year-old.
The daughters were able to escape the vehicle, which landed on its side in the river, Poore said. They stood on top of the car and got the attention of a passing kayaker, he said.
The kayaker took the girls to shore before returning for their mother and father, Poore said.
The father, 50-year-old Christian Lemler, suffered moderate to major injuries, but the injuries are not considered life-threatening, Poore said.
Lemler was taken to Marshall Hospital in Placerville.
The CHP learned of the crash when an officer en route to another accident was flagged down at about 3 p.m., he said.
The collision remains under investigation but Poore said it had been raining at the time and the roadway was slick.