"With regards to the ongoing investigation into last night's horrific attack at the Manchester Arena, we can confirm we have arrested a 23-year-old man in South Manchester," police said in a statement, according to AFP.
At least 22 people were killed and more than 50 wounded in the explosion on Monday.
Police responded to reports of the blast shortly after 10:35 pm (2135 GMT) at the arena, which has the capacity to hold 21,000 people, where a US singer had been performing to an audience that included many children.
A witness who attended the concert said she felt a huge blast as she was leaving the arena, followed by screaming and a rush by thousands of people trying to escape the building.