The deaths are reported to have happened in an off-piste area as skiers made their way through fresh snow.
Officials said the injured skiers were hit by falling rocks and had been taken to hospital by helicopter.
There have been several skiing deaths in the Alps this winter.
Rescuers on Thursday said that skiers from Germany, Belgium, Sweden and Italy were caught up in the avalanche.
A second avalanche on Thursday was reported to have taken place in the same area soon after the first. Two off-piste skiers were caught up in it, but neither was reported to have been injured.
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The avalanche risk - in one of the busiest weeks of the year for skiing in the Alps - has been assessed by officials to be three out of five, because of recent heavy snowfalls and powerful winds which have caused drifting in some areas.
Courmayeur - on the slopes of Mont Blanc - is renowned for the high difficulty levels of its skiing.
Three people have been killed, two are believed to be missing and three wounded in a major avalanche near the northern Italian ski resort of Courmayeur, reports say.