The abandoned car was found on Saturday on the side of a route 747 located about 20 kilometres west of Jokkmokk in northern Sweden.
On Sunday, authorities dispatched helicopter search and rescue teams as well as sniffer dogs in an attempt to find the vehicle's missing driver, but to no avail.
"Something must have happened to leave the car so quickly and in such a peculiar way. It's a mystery," Anders Calderäng of the Norbotten County Police told the TT news agency.
The unlocked car was rented in the Czech Republic. Inside police found bank cards, car keys, some cash and a driver's licence of the 26-year-old man believed to be the driver.
The car was due to be returned to the Czech rental agency last Thursday, but passed over the Öresund Bridge connecting Sweden and Denmark on Friday before turning up abandoned in Sweden's far north
Police have been in contact with 26-year-old's relatives in the Czech Republic, but they were also unsure of the man's whereabouts and equally curious as to what may have happened.
"It's a rather odd place to end up. And with a Ford Mustang, a white convertible – that doesn't really fit in with this rural environment," said Calderäng.
When a passerby discovered the car on the roadside near the Pärl River, they also found a set of tools and a rope in the vicinity of the Mustang.
Police are now looking into whether the 26-year-old had any acquaintances in Norbotten County that he may have planned to visit.
"We don't suspect any foul play, but the circumstances are a little strange," said Calderäng.
Anyone with information about the car, a white Ford Mustang GT convertible with Czech licence number 2AK9676, is encouraged to contact police at 114 14.