At a regular cabinet meeting, the premier urged that contingency groups be set up as the typhoon streaks towards the island.
Mindulle brushed past the northeastern Philippines on Tuesday, cutting power and telecommunications lines and inducing heavy rain that caused landslides and flooding, displacing more than 3,000 people and disrupting road traffic, rescue officials said.
Traffic between some offshore islands and Taiwan was also interrupted, while some schools in Taiwan's southern Pingtung county were shut down.
An official from the Central Weather Bureau (CWB) said: "Residents in the east and south (of Taiwan) where the typhoon may bring heavy rains and strong winds should heighten their vigilance."
Education authorities said a national exam, involving some 117,000 high school graduates on Thursday, Friday and Saturday, would be postponed if the typhoon hit any of the island's districts.
Mindulle was 310 kilometers (186 miles) south-southeast of Eluanpi, the southernmost tip of the island, at 3:00 pm (0700 GMT).
With a radius of 250 kilometers (155 miles), the typhoon was moving west-northwest at a speed of eight kilometers per hour (4.9 mph).