The latest quake hit at 5:15 am local time (1715 GMT Sunday) and occurred 205 kilometers (127 miles) southeast of the Wallis and Futuna capital of Mata-Utu, the US Geological Survey said.
It came less than two hours after a 6.4-magnitude quake struck off Tonga.
There were no tsunami alerts and immediate reports of damage.
The undersea quake off Tonga hit at 3:52 am (1552 GMT Sunday) and was 197 kilometers northwest of the town of Hihifo, USGS said.
The epicenter was also at a depth of 10 kilometers.
That tremor was followed less than three hours later by a 5.6-magnitude quake a few kilometers further west.
The region lies in the so-called Pacific Ring of Fire, an area of frequent seismic activity due to collisions between continental plates.