Even though the chances of contracting malaria on Zanzibar are low, anti-malaria precautions are recommended. Anti-malaria tablets and mosquito repellent are the most common ones.
Ask your local travel clinic or doctor for advice on how to prevent contracting malaria while travelling. There are a number of effective anti-malaria prophylaxes to choose from these days. Some anti-malaria treatments need to be started before you travel so check in with a medical professional in advance.