Typhoon Danas lashed southern Taiwan with record winds and strong rain early on Monday, killing two people and injuring more than 330 in a rare hit to the island's densely populated west coast, where businesses and schools were shut.

Taiwan is regularly struck by typhoons, but they generally land along the mountainous and sparsely populated east coast facing the Pacific.

Typhoon Danas, at one point listed by Taiwan's weather authority at the second-strongest level, headed north towards the Taiwan Strait after making landfall along its southwestern coast late on Sunday.

It has greatly weakened since and was forecast to hit eastern China later this week.

Power to more than half a million homes was cut and over 300 domestic and international flights were cancelled, government data showed.