No, officially there is no age limit to do the Annapurna Base Camp trek. However, you should be reasonably fit both physically and mentally. Children, less than seven/eight years of age are not advised for the trek. If you are taking a child below ten years of age along with you, ensure that he is reasonably fit. Try to keep the trekking itinerary light and relaxed to accommodate for their shortage of strength, pace, and endurance.