The offices of This Day newspapers in Abuja and Kaduna were bombed, This Day reported.
The first explosion went off around 11 a.m. at the office in Abuja, Voice of America reported, killing three people.
Olusegun Adeniya, chairman of This Day's editorial board, said a suicide bomber rammed a vehicle into the gate of the building, killing himself and two security guards.
In Kaduna, police arrested a man suspected of the bombing there.
Witnesses said the suspect drove a vehicle into the newspaper building and shouted "God is great" in Arabic. Three people were killed in the incident.
"When people saw, they thought he just mistakenly hit the building. They pull[ed] him out and then he was telling them, 'There is a bomb. There is a bomb,'" Kaduna resident Diji Obadiah said.
There was no immediate claim of responsibility for the attacks.