Greater Manchester Police said a 25-year-old man had been detained on suspicion of terror offences in the Old Trafford area. A search was also being carried out an address in Moss Side, in the south of the city, as part of the investigation.
Twelve people are now being held in custody after the atrocity at the Manchester Arena left 22 dead.
Images posted on social media showed armed officers in the Moss Side neighbourhood amid reports of an explosion.
Police would not comment on whether a controlled blast was used to gain entrance to the property, a tactic used on previous raids.
One resident wrote on Twitter: “There was an explosion about half an hour ago on Selworthy Road, Moss Side. There is armed police and dogs surrounding the area.”
The latest operation came just hours after the Home Secretary warned that members of bomber Abedi’s terror network could still be at large.
Ms Rudd said parts of the suicide attacker’s circle were “potentially” unaccounted for, despite optimism that a previous wave of arrests had quelled further threats.
On Saturday night, police issued CCTV stills of Abedi, bespectacled and casually clothed, in a plea for information about his movements between 18 May and the attack.
A matter of hours after he was captured on camera, the 22-year-old was dead, having inflicted an outrage on a pop concert attended predominantly by young girls.
The huge police response that followed saw raids in several cities as counter-terror efforts were focused on cornering his suspected criminal ring.
As the huge counter-terror operation continued, the NHS said that 54 people injured in the attack were still being treated in eight hospitals with 19 receiving critical care.
A total of 116 people required hospital care in the wake of the massacre, police previously said.
Another Moss Side resident, who did not want to be named, said he heard a loud explosion “like a bomb going off” and saw a number of police vans in the street.
He said a group of young Middle Eastern men moved into the address around six months ago.
“There’s a group of them knocking about with each other - they’re from the Middle East,” he added.
“A couple of them dress in the traditional Muslim robes.
“There was always a lot of coming and going in and out of that building.
“Every time I’ve been outside my flat there’s someone there or a group of them sitting outside in a car.”
Three men were arrested as police stormed the Moss Side property, but were later “de-arrested”, Greater Manchester Police said.
Yesterday US president Donald Trump said Prime Minister Theresa May was “very angry” about leaks to the US media of sensitive information about the bombing.
Mr Trump tweeted that Mrs May gave him “full details” during talks while he attended summits in Europe.
The Prime Minister said Mr Trump acknowledged the leaks were “unacceptable” when she challenged him about them.
Mr Trump said: “British Prime Minister May was very angry that the info the UK gave to US about Manchester was leaked. Gave me full details!”
Mrs May raised the issue with Mr Trump at the Nato summit in Brussels on Thursday after police temporarily suspended sharing information with counterparts across the Atlantic after the US media was repeatedly briefed about sensitive evidence.