The man was skiing off-piste around 3.45pm on Sunday for reasons not immediately known an avalanche was triggered and swept the skier down the slope.
Police said the incident occurred in an area of the resort known as Bella Tola, beneath a peak more than 3,00 metres high.
A large rescue team looked for the man on Sunday until nightfall but was unable to locate him.
Three Air Glacier helicopters were involved in the search, along with 11 local guides, five dog teams, fire fighters, security officials from the ski resort and cantonal police officers.
Weather conditions meant the search had to be lifted until Monday morning, police said.
Saint Luc is one of five Alpine mountain resorts in the Anniviers Valley near Sierre.