Residents said they were killed during the night in the town of Potiskum. Two of them had their throats slit while the third was beheaded, they added.
Officials said the victims had been working at a government-run hospital.
No-one has said they were behind the attack, but it happened in an area where the Islamist militant group, Boko Haram, has been active in recent years.
More than 600 people were believed to have been killed in 2012 by the group, which is fighting to overthrow the government and create an Islamic state in Nigeria’s predominantly Muslim north.