The National Emergency Management Agency said the blaze happened at the College of Business and Management Studies site in Konduga, which houses more than 6,200 internally displaced people (IDPs).
"The fire started at about 10:40 am (0940 GMT) from the cooking area leading to the death of three people and six others injured," NEMA spokesman Abdulkadir Ibrahim said in a statement.
Konduga is some 35 kilometres from the Borno state capital, Maiduguri.
Boko Haram's insurgency has killed at least 20,000 people and forced more than 2.6 million others from their homes since it began in 2009.
People in the camps live in makeshift tents, often made of woven dried grass draped over tree branches. Cooking is done outside over wood fires.
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