Founder of the Toronto Rabbit Cooperative. Yes, rabbits can eat apricot, but the pit/stone -- that part is dangerous for rabbits. Apricots are high in sugar (dried apricots even more so), so too much will make a rabbit sick. The House Rabbit Society recommends no more than 2 tablespoons of fresh treat food (like apricot, or carrot) per day for a healthy, normal 6 pound rabbit.