The incident happened early today in the back garden of a property on Garth Walk, off King Lane in Moortown.
Police were called to the scene at about 4.40am after two men, aged 79 and 59, were bitten by a dog.
The 59-year-old suffered “potentially life-changing” injuries in the attack.
One of the police officers attending the incident was also bitten.
Two dogs have been seized by police and enquiries are ongoing.
Two people, believed to be the owners of the dogs, have been arrested.
No details have been released regarding the breed of the dogs.
Anyone with information is asked to ring West Yorkshire Police on 101, quoting log reference 348 of September 29.