Two cows were instantly killed and another two had to be put down because of severe injuries, police said.
A decision will be made on Monday whether to destroy one of the two other cows, which suffered pelvis injuries.
The motorist, a Swiss man in his 30s, was later arrested at his nearby home after Vaud Riviera police tracked him down, according to press reports.
A licence plate came loose from the vehicle in the accident, which occurred early on Saturday morning on the road between Saint Légier and Châtel Saint Denis, a town in the canton of Fribourg.
The vehicle lurched from one side of the road to the other before ripping out a fence and careering across a field into the cows.
The vehicle then struck a water tank before the motorist steered it back onto the road.
“What revolts me is that this person fled while leaving the cows in agony,” farmer Patrick Kohli, one of the owners of the cows, told 24heures.
“One of them had broken legs and an open fracture.”
The motorist, who was driving without a licence and third-party insurance, was taken to Montreux hospital for treatment of back, shoulder and facial injuries, Le Matin reported.
He was also subjected to a blood-alcohol test, the newspaper said.
The local prosecutor’s office has opened an investigation into the case.