The latest problem follows a similar ministry report in March about sparks shooting out of an iPod Nano, he said.
The government has been working with Apple Inc. to investigate the cause, and a defect in the lithiuim-ion battery is suspected in all three cases, he said. The iPods began to overheat while they were being recharged, he said.
He declined to disclose the manufacturers of the batteries, and said it was unclear whether the same battery was being packaged in the product, which is sold all over the world.
Apple Japan did not have immediate comment.
Yoshitsune said the two latest cases involved an iPod Nano, model number MA099, which singed nearby paper in August, and model MA005, which burned a Japanese traditional "tatami" mat, in January. Both players were twisted out of shape from the heat and became unusable, he said.
Other details weren't available.
The government has instructed Apple Japan to find out the cause of the problems and report back to the government.
Lithium-ion batteries have been blamed for a series of blazes in laptops that have resulted in massive global recalls.
Apple's iPod players are extremely popular in Japan and coveted as fashion items although Japanese manufacturers produce a host of iPod rivals.
The Japan introduction of the iPhone, also from Cupertino, California-based Apple, drew long lines last month.