Greater Manchester Police said the 10 were take into custody "on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism."
Police also searched several properties in the city, including buildings housing a takeout restaurant, computer store, and telephone store. The top floors of each building have apartments.
The force said officers from the Staffordshire, West Midlands and South Yorkshire Police forces also were involved in the operation. Scotland Yard's anti-terrorism branch was not involved, the BBC reported.
It was the second major terror raid in Britain recently, reports CBS News Correspondent Steve Holt. A huge sweep around London three weeks ago led to charges against five people, and the confiscation of more half a ton of ammonium nitrate, which has been used in several major terrorist bombings.
The seizure of the ammonium nitrate fertilizer — a component of many bomb attacks, including the October 2002 explosions that killed 202 people on the Indonesian island of Bali — spurred intense media speculation about a plot to bomb civilian targets in Britain, although police have released no details of the case against the men.
Suspects can be detained without charges for a maximum of two weeks under anti-terrorism laws, but courts grant police that permission only a few days at a time.
Officers refused to comment on what prompted the raids or with whom the suspects were thought to have ties.