Five people were taken to hospital with stab injuries following the attack at the Arndale Centre around 11:15am today.
A man in his 40s has been arrested on suspicious of assault.
Pictures and videos on social media showed several officers surrounding the centre, which has now been evacuated.
One video shows an officer holding a man to the ground whilst pointing a Taser at him.
A spokesman for Greater Manchester Police said: “We can confirm that five people have been stabbed and taken to hospital.
“In these early stages we are keeping an open mind about the motivation of this terrible incident and the circumstances as we know them.
“Given the location of the incident and its nature officers from Counter Terrorism Police North West are leading the investigation as we determine the circumstances.
“A man in his 40s, who was arrested at the scene on suspicion of serious assault, remains in custody for questioning.”
Emergency services were called to the scene at 11:17am.
The shopping centre has been evacuated and trams have stopped operating at Exchange Square outside the main entrance.
A shop worker, who gave his name only as Jordan, 23, said: “A man was running around with a knife lunging at multiple people, one of which came into my store visibly shaken with a small graze.
“Soon after, security staff told all retail staff to close their doors and move the public to the back of the stores.”
Freddie Houlder, 22, from Market Drayton was in the Arndale Centre when he heard “a load of screams just outside” the shop he was in.
He said a woman then came into the shop and told others “a guy just ran past the shop and tried to stab me”.
Mr Houlder added: “Luckily she had quite a thick jacket. She thought originally it was a fake knife because of how easily it grazed off but police came in and said it was a real knife and she burst in to tears.”
He said he was evacuated several minutes later at which point he saw “a bunch of curtains covering someone seriously injured or dead, I don’t know”.
“I definitely don’t think it was gang violence because this guy was going around trying to stab random people, I believe,” he said.
The eyewitness who shot the video of a man being Tasered outside the Arndale centre told how the suspect was “screaming”.
Shop worker John Greenhalgh, 30, was travelling on one of the city’s trams when the incident happened.
Mr Greenhalgh said: “You could tell it was something quite serious. There were a lot of armed police. They were there very quickly.
“The tram was evacuated and we were put in the back of a van. We weren’t told what was happening. There was a guy sitting on the floor screaming.”
Mr Greenhalgh said the incident was eventually cleared and he could make his way to work.
The video, which was posted on social media, has already been retweeted hundreds of times.
Prime Minister Boris Johnson tweeted: “Shocked by the incident in Manchester and my thoughts are with the injured and all those affected. Thank you to our excellent emergency services who responded and who are now investigating what happened.”