Eight people remained in custody in connection with Monday's attack, in which Abedi targeted music fans at an Ariana Grande concert at Manchester Arena, killing 22 and injuring dozens.
The woman was arrested after armed police raided a block of flats in the north of Manchester, Sky News reported on Wednesday.
Police swoop on a man near to Wigan town centre.
"This evening we have been carrying out searches at an address in Nuneaton, Warwickshire, and arrested a man", the Greater Manchester Police force said in a statement.More news: The Upcoming Meeting Between Trump And Erdo an Will Probably Be Tense
British security services are also upset that Abedi's name was apparently leaked by USA officials while British police were withholding it - and while raids were underway in Manchester and in Libya, where the bomber's father lives.
"Following this arrest, a house in Wigan was raided this morning and is now being searched".
Police said the suspect had a "package" on him while witnesses reported a bomb squad arriving at the cordoned off area.
Meanwhile, Senior police chiefs in Britain reacted with anger Wednesday night after sensitive details of the Manchester Arena suicide bombing were leaked to media in the U.S.More news: Spike Lee thanks Pete Carroll for Colin Kaepernick interest
The public were warned to stay away from the area, while Wigan Infirmary issued a plea for people to try to avoid its A&E department while the incident was ongoing.
"There were a lot of armed officers with their faces covered - with balaclavas and machine guns".
"They wrestled with a man on the floor and he had a red bag".
In Manchester's St. Ann's Square, where a sea of floral tributes grew by the hour, a crowd sang the hometown band Oasis' song "Don't Look Back in Anger". Hundreds of soldiers have replaced police protecting high-profile sites including Buckingham Palace and the Houses of Parliament in London.More news: Donald Trump Increases Rhetoric Against NATO Allies at Brussels Summit
"Then they've been there all day, mainly just one or two police sat outside".
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