While carrot juice offers countless health benefits, too much of everything can cause more harm than good. According to the Web MD, drinking too much carrot juice can cause carotenemia, a transitory condition where the skin develops a yellowish tinge due to an excess of beta-carotene in the blood. Drink no more than half a glass (4 ounces) of carrot juice every day to get the advantages without taking too much vitamin A or beta-carotene.