The explosion happened Thursday as a man was having an oxygen tank filled at the store, the Bangkok Post reported.
Police Lt. Prompong Theptaptim said those who died in the blast were identified as Sak Tawarawong, 69, Pratuang Boonree, 41, and Suradech Sawarng-arom, 30.
The injured were taken to a local hospital where three were in critical condition, Prompong said.
A total of 18 buildings were damaged in the blast, Prompong said.
Supanan Sukthanorm, a relative of Suradech and Pratuang, told police that Suradech was having an oxygen tank filled to inflate balloons for a local temple festival next week.
Police said they believe Suradech dropped his tank on the ground as he was handing it to Sak, the shop owner, triggering the explosion.