Pictures taken by a Burmese freelance photographer and published in the Swedish media this week show a Carl Gustav M3 anti-tank rifle and ammunition left behind by Burmese government soldiers and recovered by Kachin rebels after recent clashes.
The weapon's serial number is clearly visible in one of the photographs.
The European Union has had a weapons embargo against Burma since 1996.
"There is an investigation underway. We have the photographs and the serial number," a spokeswoman for the Swedish Agency for Non-Proliferation and Export Controls (Inspektionen för Strategiska Produkter, ISP), Diana Malm, told AFP.
Swedish defence group Saab, which manufactures the weapon, has said it did not sell the rifle to Burma and suggested its military must have obtained it from a third party.
Saab said it was cooperating with ISP to determine which country it had sold the weapon to, and to try to trace it.
"We have told ISP that we will help them," Saab spokesman Sebastian Carlsson said.
Malm said it was "relatively unusual" that Swedish weapons end up in the hands of third parties.
She also noted that Swedish export legislation had changed over the years.
"I don't want to jump to any conclusions" about what the inquiry will uncover, but "Sweden did export weapons to Burma" prior to the weapons embargo.