Badare Akintoye, a military spokesman confirmed two female suicide bombers carried out the attacks, Xinhua news agency reported.
The explosions occurred simultaneously at the opposite ends of the local market in Madagali, causing buyers and sellers to run for safety.
Sani Datti, spokesman of the country's National Emergency Management Agency said the 67 injured were taken to the state-run Michika General Hospital for treatment, a statement said.
The market at which the attacks took place is a weekly one that sells grains, vegetable and animals every Friday.
The blasts occurred at the animal and grains sections of the market, according to Yusuf Mohammed, a senior district official.
Adamawa State police spokesman Othman Abubakar said investigation is underway on the attacks. Madagali is located 276 kilometres from the state capital, Yola.
In August 2014, the district was one of several towns seized by terror group Boko Haram but it was recaptured by the military in March 2015.
Two female suicide bombers who were members of the Boko Haram group killed at least 30 people and 16 injured when they attacked a busy motor park in Madagali on December 28, 2015.