Moisturizer can certainly harm your eyes - these are very strong chemicals, and they can do a lot of damage. If moisturizer comes into contact with the eyes it can cause rather severe irritation. In most cases, it will not do any permanent damage, but it is always better to be on the safe side. If you have happened to get some moisturizer in your eyes, the first thing you should do is of course wash it out. Flush your eyes with plain water for at least five minutes. After you finish washing it out, then you also need to look at your eye in the mirror. If you see a lot of redness, if you can't actually open your eye, if you have a lot of pain, or if your vision is still blurry, then you need to get it evaluated either by an eye doctor or go into the emergency room.