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The avalanche hit midway through Thursday morning as skiers were out taking advantage of the conditions the day after Christmas Day.
The avalanche, which police have described as of a considerable size, swept across a trail that had skiers on it at the time.
The snow drift is thought to have covered an area of around 20 metres by 50 metres.
As well as the mountain rescue services, the police and Swiss Air Ambulance are also involved.
According to the DPA news agency, the avalanche risk had been updated to three on the scale - which implies significant danger - following heavy snowfall over the course of the last few days.
The two people who were injured have been flown to hospital by the Alpine rescue service.
The search for the others, who were thought to have been buried alive under the snow drift, is continuing with a large amount of resources.
Reto Pfister, state police spokesman in the Swiss canton of Uri, told NBC News: "We believe there are more people buried but we can't say how many."
There have also been three more avalanches in the Austrian province of Carinthia today, according to a police spokesperson.
One of those avalanches happened outside the regular ski slope and buried two free riders who were off-piste.
Luckily, they managed to free themselves from within the snow drift and are not seriously hurt.
More than 60 rescue workers, as well as snow dogs and helicopters are out searching for the people who could have been buried underneath a major avalanche that came right down the secured ski slope, the police spokesman said.
However, it is too soon to make any informed comment on potential fatalities.
Meanwhile, a man was left hanging from a rope carrying two dead companions while trying to climb a mountain in Italy's Abruzzo region.
The man had been trying to climb to the summit of the Gran Sasso mountain when his fellow climbers slipped and fell to their death.
That left the third man, who was eventually rescued, in dire need of assistance from rescue squads, according to reports in the local press.
The bodies of the two men were recovered later on in the afternoon from the valley below.
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