Counter-terrorism police were leading the investigation due to the location and nature of the attack, Greater Manchester Police said.
A police spokesperson said a man with a large knife began lunging at people and attacking them, causing “nasty” injuries.
Social media posts showed a large number of officers at the scene and a suspect being Tasered.
Three people were taken to hospital with stab injuries. One of the victims suffered “serious” injuries, North West Ambulance Service said.
A 41-year-old man from the Manchester area was initially arrested on suspicion of serious assault but he was later rearrested on suspicion of the commission, preparation and instigation of an act of terrorism.
Police later said he was detained under the Mental Health Act following an assessment by specialist doctors.
Assistant chief constable Russ Jackson, of Greater Manchester Police, said: “We do not know the motivation for this terrible attack. It appears random, is certainly brutal and of course extremely frightening for anyone who witnessed it.
“At this time we do not believe that there is anyone else involved in this attack but we will be constantly keeping this under review.
“We have specially trained officers supporting those injured from the attack.
“We’ll have increased patrols, including armed patrols, in the city centre this weekend.”
He appealed for anyone who was in the Arndale at the time to send any images or footage taken from the scene via the force’s website.
A 19-year-old woman and another woman were both taken to hospital with stab injuries and their condition was described as stable by the force.
A man in his 50s was also hospitalised with stab wounds, while a woman in her 40s was treated by paramedics at the scene but was not stabbed.
Boris Johnson, the prime minister, said he was “shocked by the incident and my thoughts are with the injured and all those affected”.
Bev Hughes, Greater Manchester’s deputy mayor for policing, crime and fire, said: “I want to praise Greater Manchester’s emergency services for their swift and professional action. Our thoughts are with the five people injured.
“The scene has been secured and all emergency services are engaged in ensuring public safety – the investigation is ongoing.”
A multi-agency response has been launched following the incident, with emergency service chiefs holding a gold-level strategy meeting with local government officials.
Officers initially declared a response under Operation Pato, a plan devised to deal with a suspected marauding terror attack, however this was later downgraded, Mr Jackson said.
While the nature of the incident remains unclear, the decision to involve counter-terror police comes two years after the Manchester Arena bombing, in which 23 were killed at an Ariana Grande concert.
And in May a man was charged with three counts of attempted murder and one count of possessing a terrorist document after a stabbing at Manchester Victoria railway station on New Years Eve.
The current threat level for a terror attack in the UK stands at severe – the second highest rating that ranks an incident as “highly likely”.
The Arndale Centre itself was the site of a terror attack in 1996, when the IRA detonated a 1,500kg lorry bomb on the neighbouring Corporation Street, injuring 212 people but killing none.