No vaccinations are mandatory to enter Bhutan, but the following are recommended or should be up to date:
Tuberculosis
Diphtheria
Tetanus
Pertussis (whooping cough)
Poliomyelitis
Hepatitis B
Rabies
A yellow fever vaccination certificate is required if you have recently traveled through or transited in a country where yellow fever is endemic.
A malaria preventive treatment is also recommended, especially if you plan to visit rural areas in the south.
For more details, consult the official recommendations of the Pasteur Institute.