The ship, which has 22 crew on board, took about 12 hours to leave the ice field behind and is now heading to New Zealand, AMSA said.
The captain of the Chinese vessel had also managed to break free of the heaviest ice around the same time "and is now making slow progress through lighter ice conditions" and is in need of no assistance, it said.
The ice surrounding the Xue Long, which has 101 people on board, had been up to 13 feet thick.
The Xue Long, or Snow Dragon, had been trapped since Friday, one day after dramatically rescuing 52 scientists, passengers and journalists from the Shokalskiy using its helicopter.
The 52 were transferred to the Australian Antarctic program's supply ship the Aurora Australis, which also raced to the rescue but was unable to break through the ice to reach the Russian vessel.
In total five ships were involved in the search and rescue mission -- Akademik Shokalskiy, the French vessel L'Astrolabe, Xue Long, Aurora Australis and USCGC Polar Star.
The national Antarctic programmes and other agencies of France, China, Australia, Germany and the US helped with "actual operational responses, contingency planning or the provision of specialist data," AMSA said.
"This was a great example of the multi-lateral cooperative nature of Antarctic operations," the authority's acting chief executive Mick Kinley said.
But the diversion of several government's Antarctic program's resources to help the Shokalskiy has drawn criticism of its "Spirit of Mawson" expedition which was emulating a 1911-1914 tour by explorer Sir Douglas Mawson.
The Aurora, which was resupplying Australia's Antarctic base at Casey when it was diverted, is now running two weeks behind schedule, while French scientists have had to scrap a two-week oceanographic campaign.