Yellow Fever:
The government of Tanzania requires proof of yellow fever vaccination upon arrival if you are traveling from a country with risk of yellow fever. If you are travelling directly from the United States and transit through another country, it is NOT REQUIRED.
However if you will stay for more than 24 hours in a country that is endemic for Yellow Fever, you are required to have the vaccine. A complete list of these countries is available at the U.S. CDC website: https://www.cdc.gov/yellowfever/maps/index.html
Yellow Fever Vaccine Waiver:
If your doctor has recommended that you should not have the yellow fever vaccine due to a condition or having reached above 60 years of age, you can travel to Tanzania with your letter from the doctor and show it to the border immigration officer to waive the requirement.
Others:
The best choice of vaccines for your trip depends on many individual factors, including your precise travel plans. Vaccines commonly recommended for travelers to Africa include those against Tetanus, Diphtheria, Polio, Typhoid, Hepatitis A, Hepatitis B, Yellow fever, Malaria Rabies and Meningitis.
Certificate is required for entry into, or travel between, some African countries. Several of these vaccines require more than one dose, or take time to become effective. It is always best to seek advice from your doctor on immunization well in advance, if possible around 6 weeks before departure.