The Tainan District Prosecutors Office said Lin Ming-hui and two others, identified only by their surnames, Chang and Cheng, were suspected of negligence resulting in death, Taiwan's official Central News Agency reported.
The office requested their detention to prevent collusion or other acts that could disrupt the investigation, CNA said.
The death toll in the quake stands at 41 , with all but two of the deaths coming in the building collapse. More than 100 people are believed to still be trapped in the debris.
Shoddy construction is suspected to have contributed to the disaster, with the 17-storey Weiguan Golden Dragon, built in 1989, the only major building to collapse in the quake.
Although the shallow quake was potentially devastating, few buildings were damaged as a result of strict construction standards in force in Taiwan, an island that is frequently struck by quakes.
Most of the 320 people who were rescued from the disaster were saved in the hours immediately after the quake, in which the building collapsed on to itself before toppling over on to its side.
Among the survivors, Ko Ching-chung said he had propped himself against a wall to avoid falling on to his girlfriend after the quake hit just before 4am on Saturday. But after 20 hours, he could no longer hold on and collapsed on to her.
“She would have soon not been able to breathe,” Ko, who was rescued along with his girlfriend on Sunday morning, told reporters at the hospital where he was recovering.
Five survivors were believed to have been pulled out on Sunday, and at least four on Monday. One of them, Tsao Wei-ling, was found under the body of her husband, who had shielded her from a collapsed beam, CNA reported. Tsao’s husband and two-year-old son were found dead, and five other members of the family remained unaccounted for, the news agency said.
Teams also rescued a 42-year-old man and an eight-year-old girl.
Shortly after she was rescued, workers also pulled out her aunt, a 28-year-old Vietnamese woman identified as Chen Mei-jih, who had been trapped on what was the building’s fifth floor.