The Japan Meteorological Agency (JMA) issued the warning for the areas around Okinawa, Miyakojima and Yaeyama Islands.
“Tsunami waves are approaching the coasts. Evacuate as quickly as possible. Waves can hit repeatedly. Continue to evacuate until all warnings are lifted,” the meteorological agency said.
People are reportedly trapped in buildings after the earthquake sent buildings tipping off their foundations.
The quake off the coast of southwestern Japan has caused power outages in parts of Taiwan.
And a Tsunami warning has been issued in the Philippines.
The quake has been described as “very shallow”, which can cause more damage.
JMA forecast a tsunami of up to three meters (9.8 feet) after the quake hit at 7.58am local time.
WAVES BEGIN
About half an hour later, it said the first wave of the tsunami was already believed to have arrived on the coasts of Miyako and Yaeyama islands.
A wave of 30cm was detected on the coast of Yonaguni island about 15 minutes after the quake struck.
JAMA said waves likely also hit the coasts of Miyako and Yaeyama islands.
The earthquake was felt across the island, according to Taiwan’s Central Weather Administration agency.
It measured 7.2 at the epicentre and around four at its weakest.
Television showed buildings in Taiwan’s eastern city of Hualien shaken off their foundations. The quake could be felt in the capital Taipei.
Photographs show how the quake triggered massive landslides and caused buildings to crumble.
The islandwide train service was suspended, as was subway service in Taipei.
The quake struck on the other side of the island from the capital, but was strong enough to knock items off shelves in the city.
It comes after a magnitude 9 earthquake hit the country in March 2011, the strongest in the country’s history and triggering a massive tsunami.