Although juice fasts are generally speaking safe, you have to be aware of certain conditions that could be worsened by fasting. For example, if you have Type I (non-insulin-dependent) diabetes, gout and Syndrome X. 
Pregnant women and Nursing Mothers should never fast, but can without worry add vegetable juices to their daily diets as a breakfast or any snack.
If you feel very sick the detox could make your condition temporarily worse. Please speak to your Health Care Practitioner.