Zithromax is a trade name of Azithromycin. No, it is not addictive. There is no components in it that is addictive. For more information, it is an extremely versatile antibiotic, able to treat a number of conditions with varying courses. Its mechanism of action is it destroys the proteins in the bacteria, preventing it from spreading. This keeps the infection under control and allows the body to eradicate it.
It can be used to treat community spread pneumonia as well as a series of ear infections and conditions that stem from strep throat. It serves as an alternative to penicillin, as it treats many of the same things. This means that people who find themselves terribly allergic to penicillin still have something to keep them safe and treated.