The family of Dongporn Budkor, 32, is the first among the relatives of the four victims to take the money.
Later today, Boonchert Budkor and his wife are expected to fly all-expenses-paid from Phuket to Bangkok to claim the body of their dead daughter and to arrange her Buddhist cremation ceremony in their home province, Prachinburi.
All costs are being met by the Tiger Group, which has already paid compensation to many of the 11 people injured and others affected by last Friday morning's after-hours blaze.
It's not unusual for compensation to be offered and quickly accepted in this kind of tragedy in Thailand.
Boonchert Budkor said today that while he grieved for his daughter, he appreciated what the Tiger Group was doing and had no plans to pursue legal action.
''I think they have done the right thing,'' he said. ''They are taking responsibility for what happened.''
It's not known at this stage whether the family of a second Thai woman killed in the blaze, Nipawat Sutasorn, 36, is also going to accept the million baht in compensation.
The body of a third victim, British tourist Michael Pio Tzouvanni, 24, was the first to be identified this week from dental records.
The identity of the final victim, believed to be a Frenchman, has yet to be revealed. Forensic scientists are continuing their work in Bangkok.
The cause of the blaze has yet to be revealed. Experts have said the foam used in insulating parts of the venue was highly flammable and hastened the spread of flames and the asphyxiation of victims.