Greater Manchester Police said the man was taken into custody after a property search at an address in the Moss Side area of Manchester.
"As it stands, 10 people in total have been arrested in connection with the investigation, of which a man and a woman have since been released without charge. Eight men remain in custody for questioning," a police statement said.
Some reports indicate that the security forces are on the hunt for a second device made by Abedi which may now be with a member of this network.
In the Libyan capital Tripoli, Abedi's younger brother 20-year-old Hashem, and their father, Ramadan, are being held by special forces linked to the interior ministry.
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According to media reports, Abedi was known to UK security services, but his risk to the public remained "subject to review".
Meanwhile, national level campaigning for the June 8 general election is set to resume today after local level campaigns resumed yesterday following suspension in the wake of the attack.
Monday night's attack at Manchester Arena during the Ariana Grande concert killed 22 people and injured 119. Sixty four injured still remain hospitalised.
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