Update: After an hour, the tsunami warning was lifted and according to officials that Japanese residents must expect aftershocks and everyone was advised not to panic and stay focus.
National broadcaster NHK said waves were possible on several islands in the southern Okinawa chain after a very shallow quake centered on Yonaguni in the southwest, near Taiwan.
Witnesses said buildings swayed in Taipei but there was no visible damage in the Taiwan capital.
"We are issuing warnings via the radio," Satoshi Shimoji of the Miyako City government told NHK.
"We want residents to get as far as possible from the sea," he said.
NHK said the tsunami -- an irregular wave that alters the sea level, and not necessarily a huge event -- is believed to have already arrived at remote Yonaguni, although no details were yet available.
Live footage from coastal cameras showed sea levels had apparently not risen in several harbors within the warning zone.
The Pacific Tsunami Warning Centre said in a statement that "based on all the available data... there is no tsunami threat from this earthquake."
The US Geological Survey said the 6.6 magnitude quake, which Japanese authorities had originally put at 6.8, struck 71 kilometers (44 miles) east of Hualian, Taiwan at 0143 GMT.
Japan sits at the confluence of four of the earth's tectonic plates and registers more than 20 percent of the planet's most powerful earthquakes every year.