A police spokesman said: "A man has been arrested at the Arndale Centre".
Witnesses said people were running through nearby streets, shouting "run", The Independent reported.
She said: "It was terrible - he started smashing glass and armed police turned up".
Police say the centre has now reopened and the cordon has been lifted.
Slain Montana deputy had 3 years with department
Moore is from Summerton, South Carolina and worked for the Clarendon County Sheriff's Department from 2007-2011. Gallatin County Sheriff Brian Gootkin says a Broadwater County sheriff's deputy was killed near Three Forks.
The Arndale, which contains hundreds of shops, would have already been on high alert following the deadly blast that killed 22 people at the Manchester Arena last night.
"A man has been arrested at the Arndale Centre - This is not now believed to connected to last night's attacks", the police said on twitter.
The first victim of last night's attack has been named as 16-year-old Georgina Callandar.
Following the arrest, police carried out two separate raids on homes in suburban areas of Manchester. An explosive device went off outside the concert hall.
The attack led to a large-scale investigation by the Manchester police, who asked for drivers with dashboard cameras to hand them any film they took late on Monday. Fifty nine people were injured in the attack.