Yes, a safari is perfectly safe, provided you know what you're doing! Never forget that you're in the presence of dangerous animals, and you must play by their rules to avoid being hurt. Those wanting to do a self-drive safari should ensure they do their homework thoroughly. We recommend going on safari with a trained safari driver-guide who not only looks after you but also knows where to find the animals and can tell you details about what you're seeing.
You can learn more in Safari safety tips (not just for dummies).