The quake struck 65 miles (135 kilometers) northeast of Hihifo, Tonga, at a depth of 21 miles (35 kilometers).
"Nothing is registered on our censors for tsunami waves," according to Carol Baqui, a forecaster with the American Samoa weather service.
No tsunami warning was issued by the Pacific Tsunami Warning Center in Hawaii.
Police in the Samoan capital, Apia, said they had no reports on the temblor. "We didn't feel any earthquake," an officer, who declined to be named, said.
Julie Dutton, a geophysicist with the U.S. Geological Survey in Golden, Colorado, it was a relatively small quake.
"Right now we don't have any reports of it being felt. It's pretty far off the coast so we're not anticipating anything damaging," Dutton said.
Preliminary estimates put the quake at 6.2, but that was later downgraded to 5.9.
About 90 percent of the world's temblors occur in the so-called "Ring of Fire" - an arc of earthquake and volcanic zones that stretches around the Pacific Rim.