The avalanche hit just below Mount Everest Camp 2 around 6.30am local time, according to Nepalese tourism official Krishna Lamsal.
All those killed and missing had gone early in the morning to the area to fix ropes for climbers along the route to the 29,000ft summit.
Hundreds of climbers and guides have gathered at the base camp, gearing up for their final attempt to scale Everest early next month when weather conditions improve.
The area where the avalanche occurred - at 21,000ft - is nicknamed the “popcorn field”.
Earlier this year, Nepal announced measures to help manage the flow of climbers, minimise congestion and speed up rescue operations.
The preparations included the dispatch of officials and security personnel to the base camp at 17,380ft, where they would stay throughout the spring climbing season that ends in May.
More than 4,000 climbers have scaled the summit since 1953, when it was first conquered by New Zealander Edmund Hillary and Sherpa Tenzing Norgay. Hundreds have died during attempts to scale the mountain.