The blaze in Pingtung County was reported at around 7:40 am, and was put out shortly after 1 pm, according to an online post by the island's fire agency.
Eight victims were confirmed dead after being taken away for treatment, and another was later found dead at the scene, the agency said.
The fire broke out the same day that Typhoon Krathon made landfall in Taiwan's south, and the Pingtung County government said strong winds and heavy rains in the area made rescue operations "more difficult".
One image released by the county government showed a glowing red and orange fireball surrounded by billowing smoke, with what appeared to be a jet of water aimed at the blaze.
Another showed fire engines and firefighters in protective gear responding at the scene.
The local government said a probe had been launched into the cause of the blaze, and that firefighters continued to conduct search and rescue operations.
In October 2021 an inferno in Kaohsiung raged through multiple floors of a dilapidated 13-storey apartment block for hours, killing 46 people and injuring 41.
Authorities had said the blaze started when a woman left unextinguished incense ashes on a sofa before leaving the building. She was indicted on murder and arson charges, but ultimately escaped the death penalty.
Typhoon Krathon, meanwhile, has forced schools and offices to shut for a second day, and its effects have so far left two dead and more than 100 injured.
The typhoon was packing sustained wind speeds of 126 kilometres (78 miles) per hour and gusts of up to 162 kph just before reaching the southern seaport city of Kaohsiung, according to the Central Weather Administration (CWA).
Authorities said Wednesday that the typhoon was expected to weaken rapidly after landing, but residents of Kaohsiung were urged to take shelter.
Across Taiwan, nearly 10,000 people had been evacuated as of Thursday, according to the interior ministry.
Nine dead in Taiwan hospital blaze: fire agency
Nine people died on Thursday after a fire ripped through a hospital in southern Taiwan just as a typhoon hit, making rescue operations "more difficult", authorities said.
Nine people died on Thursday after a fire ripped through a hospital in southern Taiwan just as a typhoon hit, making rescue operations "more difficult", authorities said.
This picture taken and released by Taiwan’s Central News Agency (CNA) on October 3, 2024 shows firefighters responding to a fire at Donggang Antai Hospital in Pingtung County.