The fire burned the ceiling and walls of the shop, the spokesman said. Authorities were investigating the cause of the fire.
Kyodo News agency said the 15 dead were male customers and that the cause of death was believed to be carbon monoxide poisoning.
Quoting fire department and hospital sources, Kyodo said 10 others were injured, four of them critically.
The video rental shop has 32 individual rooms, each equipped with a bed or a reclining chair, and a television that customers use to watch videos, including adults movies, cartoons and Hollywood films. Salaried men sometimes use the rooms as a cheap alternative to hotels after they miss the last train home.
Kyodo said the 15 victims were each found in individual rooms. Public broadcaster NHK said the rooms can be locked from the inside and that smoking is allowed.
Of the shop's 32 rooms, 26 were in use when the fire broke out, Kyodo said.