Staying inside the whale for about 30 hours was believed to bring relief from aches and pains for up to 12 months, the Sydney Morning Herald reports.
It was thought to have started in the whaling town of Eden on Australia's southern coast.
The practice is documented as part of the Sydney-based Australian National Maritime Museum's special whales season.
A rheumatic patient would be lowered inside the carcass of a recently-slaughtered whale "leaving just his or her head poking out," the report said.
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A story on the incident was published by the Pall Mall Gazette (later absorbed by the Evening Standard) entitled "a new cure for rheumatism" on March 7, 1896.
It said "a gentleman of convivial habits but grievously afflicted with rheumatism" had been walking along the beach with friends when he spotted the whale, which was already cut open, and "appeared to our hilarious friend a tempting morsel of flesh".
The paper says the incident, which occurred a few years prior, gave birth to the bizarre practice.
"The whalers dig a sort of narrow grave in the body and in this the patient lies for two hours, as in a Turkish bath, the decomposing blubber of the whale closing round his body, and acting as a huge poultice," it says.
The curator of the Australian National Maritime Museum exhibit, Michelle Linder, told the paper that it was unlikely to have been "a really popular thing to do".
Rheumatism is a condition causing pain and swelling in the joints, commonly affecting the hands, feet and wrists.