TOKYO—A volcano on a small Japanese island erupted violently Friday morning, sending smoke and ash 9,000 meters into the air, the Japan Meteorological Agency said, raising its volcano alert to the highest level and telling the island’s 137 residents to leave.

An “explosive eruption” from Mount Shindake was observed just before 10 a.m. local time on Kuchinoerabu island in Kagoshima prefecture, southern Japan, the agency said. The island is located about 1,600 kilometers southwest Tokyo, and the city of Kagoshima, with a population...