Occasionally medications -- including prescription, over-the-counter, herbs and vitamin supplements -- may cause a strange body odor. Typically, this is a less common side effect of medication, but it's a possibility, and one you should mention to your doctor if you notice an odor after starting a new drug. Topamax, a medication used for migraines, is one medication that may have a side effect of body odor, according to the Migraine Awareness Group.