The Norwegian man was found at around 04:30 PM on Sunday by the Skalsvattnet lake on the Swedish side of the border, about five kilometres from the roadside resting area where he had left his car. He had a broken leg and was taken to a hospital in Norway.
On Monday, around 50 people - including military personnel and volunteers - were searching for the Danish man near the location where he was spotted by witnesses on Saturday night.
Police said the man was travelling by car with his wife. The couple spent the night in the car after it broke down near the town of Sveg. When the wife woke up early in the morning, the man was gone.
"Right now there is no indication that he has been the victim of a crime. We are presuming that he has become ill as he does not usually leave his wife in this way," said police officer Henrik Hansson.
Hansson added that the wife said her husband had recently been acting strangely and out of character.