One of the men, aged in his 40s, was stabbed in the head.
Two others, aged in their 20s, were stabbed in the body.
They are all recovering in Daisy Hill hospital with injuries not thought to be life-threatening.
Police said the serious assault happened in the Ardcarn Park area of the city at around 5am on Newry.
It was reported that “some form of altercation took place between a number of men in the street”.
Officers from the PSNI’s Reactive and Organised Crime Branch in Newry are appealing for information.
Detective Constable Skillen said: “Anyone who was in the area of Ardcarn Park, Nursery Drive or Springfarm Heights this morning and who witnessed an altercation or anyone with any information that can assist with the investigation to contact detectives at Ardmore Police Station.
“Information can also be passed anonymously via the independent charity Crimestoppers on 0800 555 111.”