Armed police are on the scene at Meteor Street in Adamsdown, and a cordon is in place.
South Wales Police confirmed a man had been stabbed and officers were "actively looking" for the offender.
His injuries are said to be serious but not life-threatening. The Welsh Ambulance Service said the man is in his "late teens to early 20s".
He was taken to the University Hospital of Wales.
A man has been taken to hospital following a stabbing in Cardiff on Sunday.