The six-year-old merino ram, nicknamed Shaun, was found wandering on farmland belonging to Peter and Netty Hazell in Tasmania's Midlands.
"He couldn't see very well because of the wool over his face, so I snuck up behind him and grabbed him," Peter said.
Netty said the sheep carries an estimated 20 kg of fleece.
"It is the heaviest sheep I've ever lifted. I just couldn't believe it, I just could not believe a sheep could have so much wool," she was quoted as saying by 'ABC News'.
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Now the farmers will determine whether Shaun could be the world's woolliest sheep.
The record for the world's most fleece-yielding animal is held by Shrek, a sheep found living in New Zealand caves, which yielded 27 kg of fleece when shorn in 2004.
Shrek was euthanised in 2011.