A 25-year-old man has been arrested on suspicion of attempted murder.
Two knives were recovered at the scene and a property is being searched in the Cheetham Hill area.
The BBC understands the security services are assisting police.
In a briefing on Tuesday morning Greater Manchester Police Chief Constable Ian Hopkins added: "Last night we experienced a horrific attack on people out to simply enjoy the New Year's Eve celebrations in Manchester.
"My thoughts are with the couple who are still being treated in hospital for their serious injuries and with the brave British Transport Police officer who was also stabbed during the attack."
The three victims were taken to a nearby hospital with "serious" but not life-threatening injuries.
A woman in her 50s suffered injuries to her face and stomach, while a man - also in his 50s - has injuries to his stomach.
Manchester Victoria railway station has reopened after the stabbings.
My thoughts are with those who were injured in the suspected terrorist attack in Manchester last night. I thank the emergency services for their courageous response.
Assistant Chief Constable Russ Jackson, of Greater Manchester Police (GMP), told reporters at a briefing at force HQ the suspect lived in the Cheetham Hill area of the city.
He said officers were carrying out a search at his address.
"There is wide reporting in the press about what the attacker allegedly said during the incident and because of this we want to be clear, we are treating this as a terrorism investigation," he said.
Adding that officers are nevertheless also "retaining an open mind in relation to the motivation for this attack", he said there was no information "to suggest at this time others are involved".
He said police were still trying to establish whether the suspect is a British national; and that "given how frenzied the attack was", they are also "obviously considering his mental health".
Police recovered two knives at the scene but do not yet know if both were used in the attack, he added.
Manchester Metrolink said services to the station are operating "to the normal pattern" but advised of "minor delays".
Officers said counter terrorism police were leading the inquiry.
Image copyrightAFPImage captionThe station was shut after the attack and police remain at the scene
The officer, a police sergeant in his 30s, was stabbed in the shoulder and released from hospital on Tuesday.
The Home Secretary Sajid Javid said he wished those injured a "full recovery".
Mr Clack also said he heard the knifeman shouting "Allah" during the attack, along with a slogan criticising Western governments.
Image copyrightAFPImage captionA man has been arrested on suspicion of attempted murder
He added he was "close to jumping on the tracks" as the attacker had a "long kitchen knife".
Greater Manchester Police, which declared the attack a "critical incident", said it understood that people would be worried but there was "no intelligence to suggest that there is any wider threat at this time".
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