The 1- to 2-month-old calf was first sighted Sunday in waters off north Sydney, and on Monday tried to suckle from a yacht, which it would not leave.
Rescuers towed the yacht out to sea, and the calf finally detached from the boat but still swam nearby, Australian Broadcasting Corp. and Channel 10 television news reported.
The calf appears exhausted but rescuers hope it will continue out to sea and search for its mother or another pod of whales.
"The outlook is not good, but we are giving the calf its only option. It can't be fed, and in fact we wouldn't know what to feed it" because it is not weaned, National Parks and Wildlife regional manager Chris McIntosh told ABC radio.