Three people were killed in a blast in Abuja, with another three killed at the paper’s offices in the northern city of Kaduna.
Witnesses say at least one was a suicide bombing, but officials say it is too early to say.
No-one has said it carried out the blasts although the Islamist group Boko Haram has staged similar attacks.
Both blasts are reported to have occurred at the offices of the ThisDay newspaper, a Nigerian leading daily.
Details remain sketchy but several witnesses, including the chairman of ThisDay‘s editorial board, said the blasts were the result of a suicide attack.
“The suicide bomber came in a jeep,” Olusegun Adeniyi told reporters at the scene in Abuja.
“[Security guards] opened the gate for them… The guy drove in through the gate and rammed into the building and exploded,” Olusegun Adeniyi said.
However, a spokesperson for Nigeria’s National Emergency Management Agency earlier said the Abuja blast appeared to be caused by a bomb planted inside the building.
The Kaduna explosion happened outside a complex housing a number of newspapers, including ThisDay.
A suspect has been arrested and is thought to be a member of the Boko Haram group, news agency AFP reports police as saying.
Footage filmed by the Nigerian paper the Daily Trust, showed a scene of confusion in Abuja as people sifted through the rubble as a number of small fires burned.
Police and paramilitary forces have cordoned off both offices, while emergency workers evacuated the injured and removed the bodies of those who died, witnesses say.
“The ceiling of our building collapsed on to our computers because of the force of the blast,” said an Abuja office worker in the building next door to ThisDay.
Boko Haram – whose name means “Western education is forbidden” – wants to establish Islamic law in Nigeria and has launched a series of deadly attacks across the country, including the capital, in the past 19 months.
Last month the group warned journalists not to misrepresent their views.
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