Another 11 sailors were rescued, it said.
The Taiwanese Defense Ministry said the Panamanian-registered ship with 21 crew members broke into two after hitting rocks off the port of Keelung. The crew members' nationalities were not immediately released.
The ministry said rescuers were looking for the missing.
Taiwan was under the influence of Typhoon Nalgae throughout the weekend. The storm pummeled the northern Philippines on Saturday before moving toward China's Hainan island.