Abdullahi Abubakar Sadiq, believed to be acting as a cameraman for the terrorist group, was arrested in the town of Uba, in Nigeria's northwestern Borno state, according to the statement.
He was suspect number 58 on the list of the 100 most-wanted Boko Haram suspects, which was released earlier this year by the Nigerian military, CNN reported.
Two other suspected Boko Haram terrorists were also arrested, the army said.
Boko Haram carries out deadly attacks in northern Nigeria and surrounded areas despite the government's efforts to halt its campaign of terrorism.
In 2014, the group kidnapped nearly 300 schoolgirls. The girls were abducted on the night of April 14-15 in the town of Chibok, in northeastern Nigeria, about a two-hour drive from the border with Cameroon.