The visitors arrived in Kaohsiung, population 2.7 million, over the weekend
The Taiwanese authorities are searching for 152 Vietnamese people who arrived on tourist visas last week and have since gone missing.
The tourists arrived in the southern city of Kaohsiung on 21 and 23 December, but all but one appear to have absconded, officials say.
Local media reports suggest they may intend to work illegally in Taiwan.
Taiwan has waived visa fees for certain visitors from Asian countries including Vietnam, in a bid to boost tourism.
This is believed to be the largest case of tourists disappearing ever since the visa programme began in 2015.
The National Immigration Agency said it had set up a taskforce to investigate the tourists and "the group behind them".
If caught, the tourists would be deported and banned from the island for between three and five years, the agency added.
Vietnam's foreign ministry told AFP news agency that it was in contact with Taiwan and would work to ensure that tourism and exchange programmes would not be affected.
Taiwan is one of Asia's big traders, and is ranked as one of the richest per capita economies in the region.
-- Courtesy of BBC News