The cars affected were all built before June 2003 with 1.6 and 2.0 motors, Peugeot said.
All the cars that caught fire had been parked with the engine off, according to the company, which said that corrosion in the electrical circuit near the servo pump had caused the combustion.
“This corrosion was created by a mixture of long-term dampness and heavily salted roads,” which is often the case across Scandinavia, the Danish Peugeot unit said.
It urged owners to “take precautions: do not leave children or pets in the car for an extended period”.
About 10 incidents with Peugeot 307s have been reported in Sweden, seven in Denmark and four in Norway, according to Peugeot in the three countries.
As a result, 8,830 cars in Denmark, almost 6,000 in Norway and just over 13,000 in Sweden will be recalled in the coming weeks.
Peugeot said any worried 307 owners could bring their cars in to their local Peugeot dealership and said Peugeot garages would extend their opening hours during the coming weekend to help accomodate concerned customers.
Owners of cars directly affected by the problem would however receive a formal letter in the mail in the coming weeks telling them to bring their car in for service.
“We will pay the costs of course. We want our customers to experience as few problems as possible,” Peugeot Sweden spokeswoman Maria Lantz told AFP.