Puppy hiccups are usually harmless. Some pups even hiccup when they are in the womb. Many puppies under 6 months hiccup a few times during the day. The hiccuping bouts usually last 2 to 3 minutes. The hiccups are usually brought on when the puppy eats or drinks too quickly. Medications, stress and excitement can also bring them on. You should bring your pup to the vet if the puppy vomits/regurgitates his/her food when hiccuping. Also contact your vet if the hiccups last longer than 30 minutes or if it happens more than a few times a day.
You can massage your puppy while he/she hiccups to relax them.
You can also change the way you feed the puppy. Reduce the speed with which he/she eats. There is a slow feed bowl that is available in pet shops. Its great for slowing the puppy's speed eating down.