Nigeria UN bomb: 'Al-Qaeda-linked' man named as suspect
It said two other Boko Haram suspects had been arrested on 21 August, five days before the bomb, following a warning of attacks in the capital.
Friday's suicide car bombing killed 23 people and wounded more than 80.
Boko Haram, which is fighting for the establishment of Sharia law in Nigeria, has claimed responsibility for the attack.
The group is alleged to have had contacts with al-Qaeda in the Islamic Maghreb, which operates in North Africa, and al-Shabab in Somalia.
"Investigation has revealed that one Mamman Nur, a notorious Boko Haram element with al-Qaeda links who returned recently from Somalia, working in concert with the two (arrested) suspects masterminded the attack on the United Nations building in Abuja," said the secret police statement.
It said Mamman Nur remained at large and appealed for information leading to his arrest, adding that the two suspects arrested on 21 August were being held at a military facility.
They were identified as Babagana Ismail Kwaljima, aka Abu Summaya, and Babagana Mali, aka Bulama, and were described as "notorious leaders of the Boko Haram extremist sect".
They were detained three days after a warning.
"On 18 August, 2011, precise intelligence was obtained by this service that some Boko Haram elements were on a mission to attack unspecified targets in Abuja," said the statement.
Loosely translated from the local Hausa language, Boko Haram means "Western education is forbidden".