Police have arrested a 26-year-old man over the incident.
The first victim was stabbed in the back and is currently in a stable condition.
The second received minor facial injuries and is also receiving hospital care.
Police were called to the incident at around 8.30pm on Thursday.
Greater Manchester Police released a statement on the attack from Detective Inspector Jen Tattersall.
She said: “This incident has left two people in hospital and we currently have one person in police custody.
“An investigation is currently ongoing to establish the full circumstances surrounding this stabbing.
“I would like to reassure the public that we have increased police patrols in the area as detectives carry out their enquiries, and we are treating this as an isolated incident with no further risk to the wider public.
“Piccadilly Gardens is a popular location, therefore we are confident that there are a number of people who may have been in the area at the time and witnessed this incident.
“If you have any information at all that could help officers to complete their enquiries, do not hesitate to get in touch.”
Anyone with information about the incident is urged to call police on 0161 856 4409 quoting incident number 2675 for 01/10/2020.
Alternatively anonymous reports can be made to Crimestoppers on 0800 555 111.
Pat Karney, a Labour Party councillor, posted a video of police tape around the suspected crime scene on Twitter.
He commented: “Serious incident at the side of Piccadilly Gardens.
“All cordoned off and trams stopped.”