Puppies quite commonly get hiccups. When puppies eat and drink, they tend to ingest large quantities of air. Air, as it enters the esophagus and stomach, tends to trigger the hiccupping response. The authors have never seen an instance where hiccups was the result of any disease disorder. Consider hiccupping normal and common in dogs, and especially in puppies less than eight months of age.
There is really nothing you can do for a puppy with hiccups, other than have him rest quietly until the hiccups are gone. If you find certain circumstances such as extreme excitement seem to trigger the hiccups, you can try to avoid those types of situations.