Images posted on Twitter show officers, their faces covered by balaclavas, holding guns and surrounding a car.
Greater Manchester Police said the man was carrying a package when he was arrested in Wigan – another image purportedly showed the package, a red bag, on the road.
In a statement, police said: ‘We have made an arrest in Wigan this afternoon in connection with the investigation into the horrific incident at Manchester Arena.
‘When arrested, the man was carrying a package which we are currently assessing.’
It is believed that bomb disposal experts have arrived at the scene to assess the package.
Six people have now been detained in connection with the attack that killed 22 people and injured more than 100 after an Ariana Grande concert.
In addition, the brother of suicide bomber Salman Abedi has been arrested in Libya.