Details were still emerging of the attack in the early hours of Tuesday in the town of Mubi, with emergency and security officers in the region having rushed to the town.
Attackers were said to have gone to an off-campus housing area and gunned down students. Police spokesman Mohammed Ibrahim confirmed 26 people killed.
A relief official said 15 people were wounded and taken to hospital, adding that the military had taken over the area.
Adamawa state, where Mubi is located, has been hit by violence blamed on Islamist extremist group Boko Haram, and Mubi itself was the site of a recent high-profile military raid targeting the insurgents.
Some officials however suggested the attack was linked to recently held student elections, though they could not explain how or why it would have become so deadly.
Nigerian officials have been seeking to show they are having success in the fight against Boko Haram with a number of raids and arrests. There had been a lull in major attacks in recent weeks.
"We are not ruling out insider involvement, although we don't know who is behind the killings yet," said Ibrahim. "We have opened investigations."
A spokesman for the National Emergency Management Agency said initial reports indicated some of the victims were candidates in the polls.
"The crisis in Mubi is suspected to have been fueled by campus politics after an election at the Federal Polytechnic," said the agency's Yushau Shuaib.
Abdulkarim Bello of the Red Cross said "they are conducting elections in the Federal Polytechnic and unknown gunmen just entered and sprayed people with bullets".
Nigeria's military said last week it had killed a senior Boko Haram leader and arrested 156 suspected members of the group during a raid in Mubi. The town had been placed under curfew during the raid but it has since been lifted.
In September, Boko Haram claimed arson attacks on about two dozen telecommunication masts across northern Nigeria, with Mubi among the areas hit. Mobile phone reception has been badly affected in some areas.
Mubi is not far from the city of Maiduguri in neighbouring Borno state, which is considered the base of the Islamist group that is blamed for killing more than 1,400 people in northern and central Nigeria since 2010.
The town has seen previous such violence, including in January, when gunmen opened fire on Christian Igbos at a house as they mourned the death of a friend killed in a shooting the night before.
Residents and a relief official reported up to 17 people dead, while police said 12 were killed, with between two and five people killed the previous night in the same town.
Boko Haram has claimed to be seeking an Islamic state in Nigeria's mainly Muslim north, but its demands have repeatedly shifted and it is believed to include a number of factions with varying aims.
Government has claimed to be engaging in back-channel talks in a bid to end the insurgency, but Boko Haram's suspected leader, Abubakar Shekau, denied dialogue had occurred in a YouTube video posted on Sunday.