Armed officers were called to the food court at Manchester Arndale at around 1.20pm on Saturday before it was evacuated but police did not find anyone with a gun.
Witnesses say they saw a man standing on a table and shouting.
One shopper told the Manchester Evening News he started “shushing everyone”, telling them to “be quiet” and saying they should “listen to him”.
He then said “can I have everyone’s attention please”, according to the eyewitness, who said the man started to undress, taking his jacket and bag off, until he was topless.
The man is described as black, in his mid to late teens, about 5ft 7in tall, of medium build, and wearing light-coloured tracksuit bottoms.
He is believed to have put his T-shirt back on as he fled from the city centre shopping venue.
Superintendent John-Paul Ruffle, of Greater Manchester Police’s Specialist Operations Branch, said: “We responded immediately to this incident, and thankfully it was quickly established there was no credible threat to the public.
“The man who caused the disturbance was not seen with any weapons, but nevertheless it caused fear and panic to quickly spread amongst people in the Arndale.
“Despite no evidence of a credible threat, we are taking this very seriously. A full investigation has been launched to establish the full circumstances of what happened and enquiries are ongoing to trace the person responsible.
“There will be increased patrols in the area, and anyone with questions or concerns is encouraged to speak to officers on the ground.
“I would urge anyone with information or footage of the incident to contact police on 0161 856 4275.”
:: Information can be passed on to the independent charity Crimestoppers, anonymously, on 0800 555 111