A party of 19 people, including four professional mountaineers, were at an altitude of over 5,000 meters when the weather turned into a snowstorm.
During the ascent, one of the climbers began to feel unwell and returned with one of the guides.
On the way down, she died in the guide's arms, according to the company that organized the mountaineering.
The rest of the group continued towards the top of the mountain.
The blizzard picked up when the group was on its way down again.
One of the climbers broke his leg, which forced the party to move slowly despite the minus degrees.
Several are being cared for in hospitals
Two people froze to death and two more lost consciousness.
They died when they were carried down during a rescue mission, which due to the weather is described as very complicated.
Several of the group are being treated in hospital with cold injuries.
Although Elbrus with its 5,642 meters high peak is not considered a particularly difficult mountain to climb technically, dozens of climbers die every year.