In footage that has emerged online, officers in black face masks can be seen arresting a man outside Morrisons supermarket in the suburb of Chorlton at about 10:30 am Tuesday.
The suspect has yet to be officially named, but police have confirmed the man is aged 23.
Meanwhile, Greater Manchester Police have named the Manchester Arena bomber as 22-year-old Salman Abedi.
Following the arrest, police carried out two separate raids on homes in suburban areas of Manchester.
A flat in Whalley Range and a house in Fallowfield were raided by armed police officers and examined by forensic teams. A controlled explosion was carried out at the Fallowfield address at 12:30pm to gain access to the home.
Police confirmed the executed warrants and controlled explosion were part of the investigation into last night’s attack.
Officers have been combing the streets of the city since being alerted to the attack that claimed the lives of 22 people and injured a further 59 in Manchester Arena.