The explosives, packed on a pickup truck parked in front of the ring, were remotely detonated by a mobile phone, according to police.
Thai Rath Online reported two women, Prissana Kwanpetch and Pinom Sim, were killed instantly.
The police said preliminary investigations found the perpetrators had driven the Isuzu truck to park near the ring when a game was about to end and then fled.
The truck was robbed from Saroj Duangsuriya, 47, who had been killed by four gunmen on motorcycles on May 28.
The officers reckoned the unrest was an effort to create unrest during Ramadan.