The tragedy occurred in Sub Sector Hanif in Turtuk area of the glacier when troops of the 1st Assam Regiment were moving between posts. All the six bodies have been pulled out of the snow.
"At around 6.15 am, our posts at a height of over 17,000 feet came under an avalanche in Sub Sector Hanif in Siachen. Six jawans lost their lives. One is missing," Army spokesman Lt Col JS Brar said in Srinagar.
"Avalanche rescue teams have been deployed, but the operation had to be stopped because of adverse weather. The search will be restarted the moment the weather clears up," he said.
The Siachen Glacier in the Karakoram range of the Himalayas is the world's highest and coldest battlefield, with both Indian and Pakistani soldiers stationed there.
There have been repeated calls to demilitarise the glacier because of the cost of maintaining troops at those icy heights and the high casualties from hostile weather.
More troops have died on the glacier due to adverse weather than combat. In April, an avalanche killed 139 people at a Pakistan Army camp.
This is the first time in several years that an avalanche has hit an Indian position in the Siachen Glacier, army sources said.
India and Pakistan have held several rounds of talks to end the military stand-off, but without success. Talks were last held in June this year in Rawalpindi, but both sides stuck to their stated positions.
Indian and Pakistani troops have been engaged in the standoff on Siachen since 1984. The guns have largely been silent since late 2003 after a ceasefire.
(With inputs from PTI)