The BBC's Will Ross in Lagos says the remote school in Yobe state was attacked overnight when students were in their dormitories.
All the victims were teenage boys and 11 others were seriously injured. Most of the school was burned to the ground.
Islamist militants have attacked dozens of schools in north-east Nigeria.
Last September, 40 students were killed at an agricultural college during another night-time raid.
Teachers at the school in Buni Yadi said the gunmen gathered the female students together before telling them to go away and get married and to abandon their education.
The name Boko Haram means Western education is sin.
The group says it aims is to replace Nigeria's political leadership and establish a new state under strict Islamic law.
Nigeria's military said on Tuesday it was pursuing the attackers.
"We assure all law-abiding citizens that we will continue to do what is necessary to protect lives and property," a statement said.
President Goodluck Jonathan condemned the killings, calling them "heinous, brutal and mindless".
Our correspondent says Nigeria's armed forces are facing increasing criticism for failing to protect civilians or to respond to raids by the militants.
Yobe state Governor Ibrahim Gaidam said more troops were needed to contain the militants.
Boko Haram has been accused of numerous attacks in the north including one earlier this month in Borno
"I have also been informed that the military here in Yobe state lack adequate number of troops on the ground."
This year close to 300 people have been killed in large-scale Boko Haram attacks.
The BBC's Isa Sanusi, from the Hausa service, says Boko Haram tends to attack schools that teach Nigeria's national curriculum, which the militants consider to be Western.
Earlier this month, militants claimed responsibility for killing a prominent northern Nigerian Islamic scholar, Sheikh Mohammed Awwal Albani, because he said the group's actions were un-Islamic.
Thousands of people have been killed since 2009, when Boko Haram launched its campaign to install Islamic law.
The latest offensive, ordered by President Jonathan in May, has been blamed for triggering reprisals by militants against civilians.
Addressing a news conference on Monday, the president defended the army's record, saying it had achieved some successes against Boko Haram and that the militants had been contained to a small area of north-east Nigeria close to the border with Cameroon.
He said the two countries were working together to stop the militants from staging attacks in Nigeria and then escaping over the border.
Correspondents say Yobe has been relatively peaceful this year, unlike neighbouring Borno state, where at least 250 people have been killed in a series of large scale attacks by the militants.
On behalf of himself and the Federal Government, President Jonathan extends heartfelt condolences to the parents and relatives of the murdered students.
Nigerian President Goodluck Jonathan has since condemned the violence;
The President wholly condemns the heinous, brutal and mindless killing of the guiltless students by deranged terrorists and fanatics who have clearly lost all human morality and descended to bestiality.
He assures the nation that his administration will not relent in its ongoing efforts to end the scourge of terrorism in parts of the country which has sadly claimed more innocent lives today.
The Armed Forces of Nigeria and other security agencies will continue to prosecute the war against terror with full vigour, diligence and determination until the dark cloud of mass murder and destruction of lives and property is permanently removed from our horizon.
Reuben Abati
Special Adviser to the President
(Media & Publicity)
February 25, 2014
Source: BBC News
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