The accident occurred in Kalmar, southern Sweden, early on Tuesday morning.
The car spun off the road and flipped into the river, taking in water.
The family – a mother and her childen aged four and eight – managed to get out of the car without help.
"We should probably be grateful that it landed in the river exactly where it did. Just a little bit further out it's much deeper," Reine Johansson of the Kalmar police told the TT news agency.
All three of the car's passengers were taken to hospital. The eight-year-old suffered damages to the head, while the four-year-old and the mother were treated for back pain.
It remains unclear what caused the car to end up in the river.