Seven other men are in custody in connection with Monday's blast, with police and security agencies working to prevent further attacks.
A controlled explosion was conducted to gain entry into the Cheetham Hill address.
British counter-terror chief Mark Rowley said Friday police had captured "a large part of the network" linked to the bombing, confirming they were holding "some of the key players" but admitting there was still some work to do. Two of those held, a 16-year-old boy and a woman aged 34, have been released without charge.
It was the worst terrorist atrocity to hit Britain since the July 7 attacks in London in 2005 and sparked a huge counter-terror probe. A total of 116 people were treated in hospitals after the attack.
Police have released CCTV images of the Manchester Arena bomber as they continue to piece together his final movements.
Senior officers have encouraged people to go out, but to remain vigilant.
Britain reduced its terrorism threat level a notch Saturday, from "critical" to "severe", yet security remained high as jittery residents tried to enjoy a long holiday weekend.
A shopkeeper said he hid up to six terrified passengers in the back of his Spar store on Oxford Road while armed police and uniformed officers attended the scene.
British Prime Minister Theresa May said on Thursday the terror threat level will remain at critical, following a suicide bombing at a concert hall in Manchester on Monday. But the deployment of soldiers on the streets in support of police will be phased out starting Monday night, May said.
Police identified Abedi, 22, who was born and raised in Manchester and has Libyan parents, as the suicide bomber in Monday night's attack.
British police are now hunting for a jihadist network believed to behind the deadly bombing of in Manchester that killed 22 people.
Manchester Islamic Centre board of trustees director Mohammad el-Khayat used a sermon before Friday afternoon prayers to strongly condemn the attack at the Manchester Arena that killed 22 people.
Hopkins says 12 locations are still being searched. She praised the city of Manchester for its strength and said she wanted her gigs to be a safe place for her fans.
More than 1,000 armed police are on standby as major events including the Football Association Cup Final and the Premiership Rugby Final are expected to draw tens of thousands of people.
In a heartfelt message on Twitter, she said she would think of the victims for the rest of her life.