Last December, a series of earthquakes off Taiwan damaged eight undersea cables, knocking millions of Internet users offline and disrupting banking services from Seoul to Sydney.
The U.S. Geological Survey measured the magnitude of the first quake at 6.5 at 01:51 a.m. local time (11:51 a.m. EDT). Taiwan's Central Weather Bureau said the second tremor followed four minutes later with a magnitude of 5.7.
The Central Weather Bureau said the epicenter of the first quake was 76 km (47 miles) southeast of the island and 27 km deep, and the second one about 10 km farther away. It measured the first quake at magnitude 6.6 and the second at 5.7.
Chunghwa Telecom, Taiwan's top telecommunications carrier, said an undersea cable to Japan was damaged and was under repair.
All communications are more or less back to normal, a Chunghwa spokeswoman said.
Taiwan's disaster centre said they had no reports of casualties.
Earthquakes are common in Taiwan but do not often cause serious damage. The worst in recent years was in 1999, when at least 2,000 people died in a quake measuring 7.6 in central Taiwan.