The plane, a 70-seat turboprop ATR Model 72, crashed near the runway with 54 passengers and four crew on board, it said.
"It's chaotic on the scene," director Jean Shen told Reuters.
The accident happened on one of the Penghu islands, also known as the Pescadores. No more details were immediately available.
Typhoon Matmo slammed into Taiwan on Wednesday with heavy rains and strong winds, shutting financial markets and schools.
TransAsia Airways is a Taiwan-based airline with a fleet of around 23 Airbus and ATR aircraft, flying chiefly on domestic routes, but with some flights to Japan, Thailand and Cambodia among its Asian destinations.
REUTERS