Wisuth Setsawat, the club's main shareholder, surrendered to police after a court issued a warrant for his arrest.
He has since been charged with violating safety regulations resulting in deaths and for allowing people into the premises who were under-age.
Setsawat faces up to 10 years in jail if found guilty of the charges, all of which he has denied.
Suriya Ritrabue, the club manager, is on the run from police investigators.
The Santika Club, which popular with young Thais, tourists and expatriates, was celebrating its final night at its location when the fire broke out.