Detectives have made a new appeal for witnesses and information in relation to the shooting in Crossmaglen in the early hours of Monday.
Sinn Fein MLA Conor Murphy said the victim is well respected in the local community and was on his way to work when he was shot.
A PSNI spokesperson said: "At around 6.30am, officers received and responded to a report that a man in his 30s had been shot in the arm and the neck whilst sitting inside a vehicle in the Ballsmill Road area.
"Colleagues from emergency services also attended the scene.
"It was reported that another vehicle pulled up, and a man with his face covered exited and shot the victim, before making off in the same vehicle.
"The victim was subsequently was taken to hospital for treatment for his injuries, where he remains in a critical condition at this time."
The spokesperson added: "A number of road closures remain in place, as police are still currently at the scene, conducting inquiries.
"We are appealing to anyone who may have any information which might help us to establish the circumstances of the incident to contact 101, quoting reference number 253 of 04/09/23."
Mr Murphy said those responsible must be brought to justice. He added: "I unreservedly condemn the shooting of a man in Crossmaglen in the early hours of Monday.
"The victim is a local man and is well respected in the local community.
"My first thoughts at this time are with the man injured and his family who will be in shock at this terrible news today. He is now being treated in hospital for serious wounds after being shot in the neck and arm as he was on his way to work.
"This was a despicable and cowardly attack by criminal elements. There is no place for these thugs on our streets."
The Sinn Fein MLA added: "A police investigation and operation is now under way in the area.
"We have been in contact with the PSNI and I would urge anyone with information on this attack to bring it forward immediately to police to assist in bringing those responsible to justice."