Mori, 20, a ballerina by training, wore a full-length fur coat at the pageant in Mexico City where she was crowned this year, People for the Ethical Treatment of Animals (PETA) said.
It is encouraging its supporters to e-mail Mori after her office refused to respond to inquiries, the US-based rights group said.
"As Miss Universe, you are expected to be a positive role model who sets a good example," PETA said in a letter to Mori. "Prove that your beauty is more than skin deep."
"By choosing to wear fur, not only are you directly responsible for the deaths of dozens of animals, you're also sending a clear message to everyone who sees you that animals' lives are less important than fashion," it said.
PETA also offered Mori weblinks to gruesome footage from dog and cat fur farms in China.
The Miss Universe Japan office referred queries to Mori's office in New York, where she is based. No one immediately could be reached at the New York office.
Mori has said she wants to use her tenure as Miss Universe to fight HIV and AIDS and that she hopes one day to perform on Broadway.
PETA is famous for its publicity stunts in campaigning for animal rights. It has frequently targeted celebrities and companies that promote fur, most visibly the British fashion giant Burberry.