He added that they worked through the night to determine identity of the suspect. Police later searched an address in the city's Cheetham Hill neighbourhood.
Sam Clack, a BBC producer who was at the train station, told the BBC that the police detained the suspect with pepper spray and a stun gun.
"I heard the guy shout, as part of a sentence, as part of a sentence, he shouted, 'Allah.' And then I thought, that doesn't sound good," he said, referring to the Arabic word for God.
Clack also later tweeted that the suspect had a "long kitchen knife".
The BBC also broadcast video footage of the suspect shouting "God is greatest" in Arabic as he was being taken away by police.
Manchester was the scene of a devastating suicide bombing at an Ariana Grande concert in 2017 that killed 22 people.
British Prime Minister Theresa May tweeted that her "thoughts are with those who were injured in the suspected terrorist attack in Manchester last night" and she thanked emergency services for their "courageous response".
Elsewhere in Europe, a driver rammed his silver Mercedes into a group of people in the German city of Bottrop.
Authorities said that at least four people were injured, including Syrian and Afghan citizens. A 50-year-old man was arrested on suspicion of carrying out a xenophobic attack.