The college earlier said that the cub, named Boo Boo, would have to be euthanized in order to test it for the disease.
The cub was brought to the campus of Washington University in St. Louis, Missouri, on Sunday along with some other animals from a petting zoo to help students relax before final exams, the university said in a statement.
Health officials previously said they couldn't rule out the possibility the cub had rabies, the university said.
If it tested positive, students would have been advised to get vaccinated for rabies, a life-threatening viral disease.
Late on Friday afternoon, the university issued a news release stating that local, state and federal health officials determined that Boo Boo posed no rabies threat and that students will need no treatments.
"We are thrilled that this very unfortunate situation has come to the best possible conclusion for everyone involved - our
students, our community and the bear cub," said the release issued by university spokeswoman Susan Killenberg McGinn.
Animals from the local petting zoo have been brought to the private university in St. Louis for several years during exam time, but Boo Boo was included this year without the school's knowledge, administrators said earlier.
(Reporting by Kevin Murphy in Kansas City, Mo.; Editing by Sharon Bernstein and Andrew Hay)