The suspect was arrested along with two other people at a checkpoint in the northeastern city of Gombe, the military said in a statement Wednesday
One of the other suspects was shot trying to escape, the military said, without saying whether the shooting was fatal.
The statement didn't identify any of the suspects by name or give details on why the military believes one of them orchestrated the deadly bombings.
Military and state security operatives had trailed the man, described as "a highly placed terrorist," before he was caught hiding in a trailer at the checkpoint, the statement said.
He is suspected of masterminding bombings in the central Nigerian city of Jos on Sunday and in the north-central city of Zaria on Tuesday.
The Jos attacks
, one on a restaurant and one on a mosque, killed at least 44 people, according to authorities. The Zaria bombing
hit a local government office, killing at least 26 people, officials said.
No group has claimed responsibility for the attacks. But the Islamic extremist group Boko Haram has been linked to deadly attacks in Jos in the past.
The military's statement Wednesday on the arrests didn't mention Boko Haram by name.
Government open to talks with Boko Haram
Northern and central Nigeria have seen frequent attacks on civilian and government targets since last week, leaving more than 200 people dead.
Witnesses and government officials have blamed last week's attacks on Boko Haram, the terrorist group that has been fighting the Nigerian government for more than a decade, pushing to bring an extreme version of Islamic law, or Sharia, to the masses.
Amid the growing death toll, Nigerian President Muhammadu Buhari's government has said it would be open to talks with the militants.
"Most wars, however furious or vicious, often end around the negotiation table. So, if Boko Haram opts for negotiation, the government will not be averse to it," Femi Adesina, a presidential adviser, said in a recent statement.
Buhari was elected earlier this year and pledged to focus on the fight against the Islamist group, which has pledged allegiance to ISIS. But so far, he has struggled to stem the heavy bloodshed in northeast Nigeria and beyond.