The man was arrested at the scene after five people were stabbed in the Arndale shopping centre this morning.
Counter terrorism police are leading the investigation but GMP said it is keeping "an open mind" about the the motive for the attack.
Five people have been taken to hospital with stab injuries following the attack at around 11am.
A spokesman for Greater Manchester Police said: "Specialist officers are continuing to respond to an incident at the Arndale shopping centre in Manchester city centre.
"We can confirm that 5 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."
North West Ambulance Service said it has treated four people, including one patient with serious injuries. All have been taken to hospital.
A spokesman said: "We are still on the scene. It is a stabbing incident.
"We've got quite a few resources there.
"We have treated four patients, including one patient with serious injuries and all have been taken to hospital."
Police officers were seen descending on the shopping centre and a video of a man being tasered has been shared on social media.
Manchester Arndale confirmed that the shopping centre was evacuated and put in lock-down.
David Allinson, director of the shopping centre, said: "A serious incident has taken place at Manchester Arndale this morning.
"The centre has been evacuated while police investigate the incident.
"We are unable to comment any further as the incident is currently being handled by Greater Manchester Police, who we will continue to support with their investigation."
Witnesses at the shopping centre described seeing a knifeman run amok in the shopping centre, 'lunging at people' at random.
One 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."
Another eye witness wrote on Twitter: "Three people just got stabbed in the Starbucks in Manchester Arndale and it’s all been evacuated. This is actually crazy."
"Just been evacuated from the Arndale. Scary stuff. Instant lock-down by staff. Sirens everywhere", said another.
The Arndale Centre is just a few hundred yards from the Manchester Arena and Victoria railway station - both of which have been the scene of recent terror attacks.
Twenty-two people were killed in May 2017 when Salman Abedi detonated a suicide bomb in Manchester Arena following an Ariane Grande concert.
The youngest victim was eight-year-old Saffie Roussos from Leyland.
Last New Year's Eve, three people, including a police officer, were seriously injured after a 25-year-old man launched a knife attack on passers-by at the same station.
The suspect was heard to shout "Allah" and "Long live the Caliphate" during the incident - he was arrested on suspicion of attempted murder and has since been detained under the Mental Health Act.