Three people were stabbed in the incident, which happened on Friday morning (October 11).
Greater Manchester Police confirmed four people in total were hurt in the incident.
A spokesperson said: "A 19-year-old woman was taken to hospital with stab wounds.
"Another woman was also taken to hospital with stab injuries. Both their conditions are described as stable.
"A man in his 50s has also been taken to hospital with stab wounds.
"A fourth victim - a woman in her 40s - who was not stabbed - has been assessed and did not need to go to hospital following assessment by paramedics.
A man in his 40s - who was arrested at the scene on suspicion of serious assault - remains in custody for questioning.
In an update, Greater Manchester Police Assistant Chief Constable, Russ Jackson, has said that the man has been arrested on suspicion of the commission, preparation and instigation of an act of terrorism.
The North West Ambulance Service (NWAS) has been stood down from the incident.
A spokesman said: "We have been dealing with the incident alongside Greater Manchester Police since 11.15 until 13.56 today.
"A large number of staff have been involved and we dispatched 13 ambulances, four hazardous area response vehicles, two advanced paramedics, two doctors and two officers to the scene.
"We would like to thank the public for their assistance and patience whilst we dealt with the incident, and express our gratitude to all our staff who have worked hard over the last few hours."
Staff that work in the shopping centre have also been told it won't reopen today.
Tina Concar, 52, from Miles Platting, Manchester, said she was evacuated from the Arndale Centre after the attack.
She said: "We only knew something was unfolding as loads of people started running towards us, at first shouting 'bomb'.
"But then someone mentioned that a person had been stabbed.
"People were panicking and running as security staff were running the other way."
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."
Labour leader Jeremy Corbyn has thanked the police and emergency services that were involved in responding to a knife attack in Manchester's Arndale shopping centre.
"Terrible reports of multiple stabbings at the Arndale Centre in Manchester," Mr Corbyn tweeted.
"My thoughts are with all those injured and their loved ones. Thank you to the police and emergency services who have swiftly responded and are doing all they can to save lives."
Home Secretary Priti Patel tweeted: "Very concerned by the incident in Manchester. My thoughts are with those affected.
"I am, as always, very grateful to the police for running towards danger to keep us safe. Now important they are given space to carry out their investigation."