The decision follows questions in Hungary over the deal. Defence Minister Imre Szekeres launched an inquiry into possible bribery connected to the 2001 agreement.
Now, Swedish prosecutor Christer van der Kwast has started an investigation into the alleged bribery, according to SVT.
The planes are made by Swedish company Saab, although at the time of the alleged bribery they were produced in a joint venture with British company BAE Systems.
"We do not consider that we have committed any irregularities or malpractice, and we have maintained this all along," said Saab spokesman Peter Larsson.
Hungary is currently leasing 14 planes, which it is due to buy outright in 2016. An investigation into a deal to lease Gripens to the Czech Republic has also been in the spotlight. Swedish authorities, as well as authorities abroad, have been investigating the agreement.