Police were called to Harehills Road at about 10.30pm last night (Sunday) after paramedics found a man injured in the street.
The 35-year-old was taken to hospital with "serious head injuries" and remains in a critical condition.
He is believed to have been punched during an altercation in Harehills Road, at the junction with Conway Place, a spokesman for West Yorkshire Police said.
A 42-year-old man has been arrested in connection with the alleged offence and is currently in custody.
Detective Chief Inspector Ian Scott, of West Yorkshire Police Homicide and Major Enquiry Team, said: “The victim remains critically ill in hospital and we are continuing to monitor his condition.
“We are carrying out extensive enquiries to establish the full circumstances surrounding the incident in which he has been injured.
“Our investigation is in its very early stages and, while we are already speaking to a number of witnesses, we would like to hear from anyone else who has seen what happened.”
A police scene is now in place in the road for forensic examinations.
Anyone with information is asked to contact police on 101, quoting Operation Polarfield.