Not if done properly. Although executed with appreciable energy, a good, clean fencing attack hurts no more than a tap on the shoulder. The force of the blow is normally absorbed by the flex of the blade. Reckless and overly aggressive fencers can occasionally deliver painful blows, however. Fencing *is* a martial art, so you should expect minor bruises and welts every now and again. They are rarely intentional. The most painful blows tend to come from inexperienced fencers who have not yet acquired the feel of the weapon.
The primary source of injury in fencing is from pulled muscles and joints. A proper warm up and stretching before fencing will minimise these occurrences.
There is a minor risk of being injured by broken weapons. We’ve never had any injuries.
The shards of a snapped blade can be very sharp and cause injury, especially if the fencer doesn’t realize immediately that his blade is broken and continues fencing. Always wear proper protective gear to reduce this risk. FIE homologated jackets, breeches and masks are ideal, as they are made with puncture-resistant fabrics such as kevlar. If you cannot afford such extravagances, use a plastron (half-jacket worn beneath the regular fencing jacket), and avoid old and rusty masks. Always wear a glove that covers the cuff, to prevent blades from running up the sleeve.
Fencing is often said to be safer than golf. Whether or not this is true, it is an extraordinarily safe sport considering its heritage and nature.