Six of those trapped were members of Japan's Ground Self Defence Force (SDF) engaged in training manoeuvres, the Defence Ministry said. All six were rescued but some were injured, it said.
Japanese media reported that as many as 15 people were injured, many apparently due to the volcanic rocks. The Fire and Disaster Management Agency said two people were seriously injured, with further details yet to be confirmed.
Three others caught in the avalanche were also rescued, Japanese media said. More searchers, including SDF members, were heading to the site near the hot springs resort town of Kusatsu to look for the missing skier as heavy snow fell.
Kusatsu-Shirane, a 2,160-metre (7,090 ft) volcano, appeared to have erupted on Tuesday morning, the Japanese Meteorological Agency (JMA) said.
The Fire and Disaster Management Agency warned that rocks could be thrown as far as 2 km (1 mile) from the peak.
Video footage from the top of the resort's gondola showed black rocks plummeting through the sky, followed by a curtain of black smoke. A photograph taken at the site on national broadcaster NHK showed a gondola with a shattered window.
"Based on various measurements, we can say that the mountain appears to have erupted, but we are still trying to confirm facts on the ground," a JMA official said.
The warning level for the peak was raised to 3, warning people not to climb the mountain.
Four people riding a gondola on the slopes were injured by broken glass, chief cabinet secretary Yoshihide Suga told a news conference, but he had no further details.
Japan has 110 active volcanoes and monitors 47 of them around the clock. In September 2014, 63 people were killed on Mount Ontake, the worst volcanic disaster in Japan for nearly 90 years.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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