The operations took place in Longsight, Fallowfield, Levenshulme, Deane in Bolton, Stalybridge and a hotel near Heathrow Airport.
Those arrested are aged between 21 and 62 and the arrests relate to the incitement of terrorism overseas.
Police said armed officers were not used in the raids, which took place at about 0400 GMT.
No arrest was made at Stockport Road in Levenshulme, but an address was searched.
Assistant Chief Constable Dave Thompson, from Greater Manchester Police, said: "This is a complex and ongoing investigation, which has now reached the point where it was necessary to make arrests and speak to a number of people.
"There was no direct threat against Greater Manchester and the arrests are the latest stage of a thorough investigation.
"We have been liaising with local people to provide reassurance about what has happened and will continue to keep a high profile presence in affected areas."
Those living in nearby communities would see a "high-profile police presence", with police distributing letters around the areas concerned and speaking to residents to let people know what has happened, the force said.