The incident happened on King's Road at 2pm and the victim is in a serious condition.
West Yorkshire Police said:
"At 2pm today police were contacted by the ambulance service who had received a report of a man with serious knife injuries in Kings Road, Hyde Park.
"Police and ambulance attended and the 32-year-old victim was taken to hospital in a serious condition.
"A scene is currently in place in the vicinity of Kings Road and Royal Park Road and enquiries are ongoing.
"Anyone who witnessed the incident or who has any information is asked contact Leeds District CID via 101 quoting crime reference 13180550009 or call the independent charity Crimestoppers anonymously on 0800 555 111."