The victim had to have trauma care at the scene before he was taken to hospital accompanied by Air Ambulance medics.
Emergency services received 999 calls to reports of a stabbing at the junction of Welsh Walls and Brynhafod Road in the town just before 1am.
Brynhafod Park was cordoned off with police guarding the entrance to the open land, popular with morning dog walkers.
A spokesperson for West Midlands Ambulance Service said crews arrived to find a male with serious injuries.
"An ambulance, a paramedic officer, a doctor and critical care paramedic from the Air Ambulance service and resources from Welsh Ambulance Service attended the scene," a spokesperson said.
"The man was given trauma care on scene before being conveyed by land ambulance on blue lights to hospital by our Welsh colleagues, accompanied by The Air Ambulance Service medics."
The victim's age and his condition are not known.