The 23-year-old was held on suspicion of terror offences at an address in Shoreham-by-Sea in the early hours of today, Greater Manchester Police (GMP) said.
United States federal agents had reportedly been monitoring Abedi since a year ago and had passed on information from Libya.
Counter-terror officers stormed addresses in Gorton, Rusholme and Moss Side and explosions were reported at several of the searches, but police would not comment on whether controlled blasts were used to gain entry.
Sunday afternoon (local time) Greater Manchester Police carried out further raids.
Manchester-born Abedi, of Libyan origin, injured more than 100 people when he detonated his explosive as concertgoers left a show by USA teen idol Ariana Grande.
Joan was with her daughter in the English city last week when a suicide bomber detonated an explosive outside the Manchester Arena, shortly after Ariana had concluded a concert there.
A woman and teenage boy arrested by British police this week have been released without charges.
Making his grim last journey these police photographs show the 22-year-old Manchester bomber, Salman Abedi en route to complete his awful act of carnage at the Manchester Arena.
Authorities over the weekend published CCTV images of Abedi on the night of the attack, which show him wearing a hat, glasses and a dark top.
Despite the terror threat being reduced from critical to severe on Saturday, she confirmed that members of Abedi's terror network could still be at large. The straps of a knapsack are visible on his shoulders.
"My prayers, thoughts, meditations & strength has been focused on those families and victims affected by the horrific tragedy in Manchester", Grande wrote Sunday afternoon in a Tweet to his 1.15 million Twitter followers.
Security remained high at major events across Britain on Sunday, including the Great Manchester Run road race, where police armed with submachine guns protected participants and spectators.
A senior Whitehall source previously has said Abedi was a "former subject of interest" to the security services whose risk "remained subject to review". "I believe we can get them to be more successful in working with us to find a way of getting some of that information", she said.
The family of one victim, 18-year-old Georgina Callander, said her life had been cut short by "evil, evil men prepared to ruin lives and destroy families".