BBC NEWS | Asia-Pacific | Asia phone links start to recover
Two people were killed in the quake
Businesses and internet providers reported sporadic problems, as phone companies warned it could take weeks to repair damaged undersea cables.
The earthquake, of magnitude 7.1 according to the US Geological Survey, struck off Taiwan's southern coast.
Services in Taiwan, Hong Kong, China, South Korea and Japan have been hit.
An official with Taiwan's largest phone company, Chunghwa Telecom, said most of the region's internet and phone services would be restored on Thursday, as operators switched traffic away from the damaged cables.
"We are renting transmission capacity from private cable operators," said Wu Chih-ming.
But millions of internet and phone users from South Korea to Hong Kong continued to encounter problems and delays.
Hong Kong's government asked people not to log on to overseas sites unnecessarily.
An official with Hong Kong's Telecommunications Authority said all seven of the submarine optical fibre cables serving the territory had been affected.
"Six of them have been completely damaged and there is a remaining one with a limited capacity," said Au Man-ho.
Ships have been dispatched from both Taiwan and Hong Kong to repair the damaged cables.
Engineers said that process could take two to three weeks, although most people will see services back to normal before then.
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