Around 20 skiers, all non-Italians, were in the area where the first snow slide occurred just before 1:00 pm (1200 GMT) in the middle of what is one of the busiest weeks of the year for skiing in the Alps, according to media reports.
A second avalanche followed an hour later in a different area, engulfing two off-piste skiers, according to the reports.
"The (first) avalanche killed three, injured three people who were taken to hospital by helicopter and left two slightly hurt," alpine rescuers said in a statement. "All were skiing off piste."
The avalanche risk had been put at three on a one-five scale as a result of fresh snowfalls and high winds which led to build-up of drifts in certain spots.
Courmayeur is located in northwestern Italy and is famed for its challenging skiing on the southern slopes of Mont Blanc.