The three female students were evacuating a first-floor hallway Saturday afternoon when they suffered the burns to their feet, a school spokeswoman said.
The Boston Herald said the hot water pipe was part of the heating system for three dorms, which were then left without heat.
Officials brought in temporary space heaters for the three dormitories, the Herald said, and crews are expected to repair the broken pipe Sunday.
The injured students, who were not identified, were taken to local hospitals and then transferred to Boston hospitals, the Herald reported.
"I was devastated to learn three of our students suffered serious burns when this pipe failed," UNH President Mark Huddleston said in a statement. "We have reached out to their families and will provide whatever assistance we can to help them through this difficult time."