Satellite photos and a video on the AMSA website showed a large part of the stern of the yacht torn away.
"The vessel departed from Vanuatu and was bound for Cairns (Australia) when contact was established. Both hulls of the vessel have been damaged following several shark attacks," the AMSA said.
Rescue crews responded to an emergency positioning beacon registered to the Tion, a nine-metre inflatable catamaran on a round-the-world expedition, early on Wednesday morning.
The yacht was located about 835km southeast of Cairns in the Coral Sea.
AMSA requested the assistance of a Panama-flagged vehicle carrier, which successfully conducted the rescue.
The three men on board the boat were unharmed, said Anna Kosikhina, a spokesperson for the voyage, which she said was aimed at promoting Russia and Siberia and began two years ago.
"They were all intact. Nobody is hurt. The only thing is that the balloons of the inflatable catamaran were blown away."
This was not the first accident on the voyage, Kosikhina said, with the steering device of a previous vessel failing during a previous leg from Chile to Easter Island.
The crew continued the expedition on an inflatable catamaran by the same manufacturer that had been stored on the island for several years.
