The arrest was made following searches at an address in the town of Nuneaton in central England, and is the first outside the Manchester area.
"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.
"These searches are connected to Monday's attack on the Manchester Arena, but this is a fast-moving investigation and we are keeping an open mind at this stage.
All the previous arrests were made in and around Manchester in northwest England where the suicide bombing took place.
More From This Section
After arresting a 23-year-old man on Tuesday, police said they had taken three more men into custody yesterday in south Manchester, the area where Abedi lived.
A fifth man who was carrying a suspect package was then detained in Wigan, northwest of the city.
The woman being held was arrested by police in Blackley, an area north of Manchester city centre yesterday.