The plane, a 70-seat ATR 72, crashed near the runway on the small island of Penghu, west of Taiwan island, with 54 passengers and four crew on board. Ten people were injured and taken to hospital.
"Today is a very sad day in the history of Taiwan aviation," Taiwan President Ma Ying-jeou said in a statement.
"All of Taiwan is grieving."
China's president, Xi Jinping, who is on a Latin America tour, felt "deeply grieved" after learning the tragedy has caused heavy casualties, the mainland's State Council Taiwan Affairs Office, said in a statement, according to the Xinhua news agency.
The mainland and Taiwan have been rivals for decades, with the mainland regarding Taiwan as a renegade province, though commercial relations have grown in recent years.
Shares of TransAsia Airways fell 7 percent at the opening bell. The main index was up 0.1 percent.
Of the 48 victims, two were French nationals, the French foreign ministry said in a statement.
The aircraft took off from Taiwan's southern city of Kaohsiung, headed for the island of Makong, but crash-landed in Huxi township of Penghu County, the main island of the chain also known as the Pescadores.
Typhoon Matmo hit Taiwan on Wednesday, bringing heavy rain and strong winds, shutting financial markets and schools. It later passed the island and headed into China, downgraded from typhoon to tropical storm.
TransAsia Airways is a Taiwan-based airline with a fleet of around 23 Airbus and ATR aircraft, operating chiefly short-haul flights on domestic routes as well as to mainland China, Japan, Thailand and Cambodia, among its Asian destinations.