"The ship was starting to head out (to the open ocean) when the blizzard hit," expedition spokesman Alvin Stone told AFP.
"It's just stuck in ice. There's no danger at all."
The ship is in the Australian search and rescue region, prompting authorities to issue a broadcast to icebreaking vessels in the area and three with icebreaking capability have responded.
The three, which include the Australian Antarctic Division's Aurora Australis, are en route to the area with a Chinese-flagged vessel expected to reach the trapped ship first late Friday.
AMSA said the mission to reach the ship could be difficult.
"It's quite windy and there could be some sort of blizzard conditions," Andrea Hayward-Maher told the Australian Broadcasting Corporation.
"Weather conditions, if they become difficult, could hinder the options that we have.
"But hopefully those icebreaking vessels will be able to get there as soon as they possibly can to render assistance."
The group on board the Russian ship are scientists and tourists recreating the historic voyage of explorer Sir Douglas Mawson to Antarctica a century ago.They have been replicating the scientific experiments his team conducted during the 1911-1914 Australian Antarctic Expedition -- the pre-eminent scientific expedition of its time to South Polar regions.
It is not known whether the ship, which is stranded just three kilometres (two miles) from open ocean, will continue with its scientific experiments once it is freed or head back to New Zealand where it had been due to arrive on January 6.
Stone said the mood on board appeared to be normal as they waited for an icebreaker to reach them.
"They have been celebrating Christmas," he said.