Media reports have identified him as Sgt. Mark Salesse, 44, of 17 Wing at Canadian Forces Base Winnipeg.
Capt. Bettina McCulloch-Drake says a soldier was on a routine mountain training exercise Thursday when he was caught in an avalanche.
She says they are hopeful he is found safe, but adds they've been told the weather is "problematic."
Parks Canada, who is leading the search, says an "incident" occurred on the Polar Circus ice-climbing route.
It says searchers were unable to get to the area on Thursday night due to avalanche hazard, deteriorating weather and nightfall.
Parks Canada says it was trying to do a helicopter search of the area on Friday because a ground search was impossible due to avalanche conditions.
"At the moment we are hopeful he will be found safe," McCulloch-Drake said Friday, declining to confirm any details about the military member's identity.
A dog handler and searchers from Parks Canada Banff, Yoho, Kootenay and Jasper are involved in the search.
According to a military news release in 2011, Salesse was badly injured during another training exercise that year when he fell from an ice wall near Ouray, Colo.
At the time, Salesse was with 5 Wing Goose Bay, N.L. He suffered injuries to his lower back, ribs, leg and pelvis.
Salesse was also stationed for a time at CFB Comox in British Columbia, and has been a member of the Governor General's Foot Guards in Ottawa. He won a Governor General's Medal for bravery for service in Croatia.