The 24-year-old was arrested after the attack at Manchester Arena, as police looked for evidence of a terror network in the area.
A total of 18 people were arrested after the suicide attack on 22 May that killed 22 people and injured 116 as they left an Ariana Grande concert.
Ten men still remain in custody.
Attacker Abedi, 22, detonated a home-made bomb in the arena's foyer just after 22:30 BST.
The blast killed young people attending the event and friends and family who were waiting to meet them.
Abedi was one of three siblings and was born in Manchester to a family of Libyan origin.
His older brother, Ismail, was arrested the day after the bombing after a raid by police in Whalley Range, but was released without charge on Monday.
Abedi's younger brother Hasham, 20, was detained in Tripoli on suspicion of links with the so-called Islamic State group on the same day.
Reuters news agency told the BBC that Abedi's father, Ramadan, had also been detained in Libya.
Ismail Abedi, the brother of Manchester bomber Salman Abedi, has been released without charge.