Nepal's Department of Tourism official Meera Acharya said at least one Chinese national injured in the avalanche was rescued by helicopter.
The avalanche hit along the popular Annapurna circuit trekking route, which encircles Mount Annapurna.
Acharya said efforts were being made to rescue the others. So far, rescuers have been able to pluck 30 trekkers who were trapped by the avalanche blocking the trail and flew them to a safe area.
Weather conditions were poor with temperature dropping in the last two days, making the operation more difficult.
The South Korean Ministry of Foreign Affairs said the avalanche hit at an altitude of 3,230 meters (10,600 feet) before noon Friday. It said five other South Korean members of the same team were safe and taking shelter in a lodge.
The missing trekkers — two women in their 30s and 50s and two men in their 50s — were teachers who were staying in Nepal for volunteer work, the ministry said, according to South Korea's Yonhap news agency.