Mohammed Zangina was detained in the Government Reserved Area (GRA) of the north-eastern city of Maiduguri on Sunday afternoon, a statement said.
Mr Zangina, also known as Mallam Abdullahi and Alhaji Musa, was planning "deadly attacks" against civilians and security personnel there, it added.
Boko Haram is fighting to overthrow the government and create an Islamic state.
The group has admitted being behind a number of attacks against churches and other establishments since 2009. More than 600 people were killed last year year in attacks blamed on it.
The military statement said Mr Zangina was leader of Boko Haram in the "North Central part of Nigeria and co-ordinator of most of the suicide attacks and bombings in Abuja, Kaduna, Kano, Jos and Potiskum".
He was also a key member of the group's Shura Committee, and a 25m naira ($159,000) reward had been offered for his capture, it added.
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