Police said five male suicide bombers detonated explosives at the camp which is located at the Muna Garage area of the city in the early hours of Wednesday.
Those wounded were taken to hospital to receive treatment.
The blasts triggered fires which burned down tents in the vast Muna camp, Tijjani Lumani, a coordinator at the camp told the AFP news agency.
"There were four explosions inside the camp. The bombers struck at different locations around 4:30 am." Lumani said.
There was no immediate claim of responsibility but Maiduguri has been frequently targeted by fighters of the Boko Haram armed group.
According to eyewitnesses, the bombers had sneaked into the camps late on Tuesday night alongside those who sell charcoal to refugees, who use it to cook their food.
Most of the people living there are those who have fled their homes due to the spate of attacks by Boko Haram in the country's northeast.
Wednesday's blasts were the latest blamed on suicide bombers, who continue to pose a threat to civilians despite military claims of success against Boko Haram.
Four people were killed on Saturday when suicide bombers blew themselves up in a village near the city.
On Tuesday, Nigerian President Mohammadu Buhari met security chiefs in the capital Abuja to review the security situation in the country. The nearly seven years Boko Haram crisis topped the agenda of the review, according to a presidential aide.
Maiduguri, the state capital of Borno state, is the birthplace of the Boko Haram insurgency, which has claimed the lives of over 20,000 people and forced 2.6 million from their homes since 2009.