The woman was reported to have died of massive blunt force. Her dog was found guarding her body.
20 Minuten said a 38-year-old man had been arrested in the region of Schaffhausen in northeastern Switzerland on Friday night as he was driving the victim's car.
The illegal immigrant who had a police record was stopped by border guards.
The weapon thought to have been used in the crime was located in the car.
A police spokesman said the motive for the crime was not clear and there were no indications that the man knew the victim.
The 66-year-old woman was named as vet Regina Z. from Brügg in the canton of Bern.
The acquaintance who found the victim's body in the wood told the Bieler Tagblatt paper that the woman's dachshund dog had been the most important thing in her life next to her job.
The forest trail is popular with dog walkers and the woman's death had caused worry among local residents.