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20 April 2019, 07:00 | Updated: 20 April 2019, 07:04
The victim managed to make his way back into his address on the outskirts of Holyhead and raise the alarm shortly before 12.35am on Friday.
North Wales Police said they were later called by staff at Ysbyty Gwynedd hospital in Bangor who concluded he had sustained injuries consistent with being shot by a crossbow.
Detectives are appealing for witnesses to the incident near South Stack Road which they described as a remote location.
Detective Chief Inspector Brian Kearney said: "The property is in an extremely remote location near to the junction of Porthdafarch Road and Plas Road.
"He was outside his home as he was attempting to fix a satellite dish when he was hit.
"He managed to make his way into his home where the alarm was raised at 00:34 and colleagues from the Welsh Ambulance Service transported him to Ysbyty Gwynedd in Bangor where he remains in a critical condition.
"We are appealing to anybody who may have been in the vicinity of South Stack Road between 6pm yesterday evening and 4am today to come forward.
"We are also keen on speaking to anybody who may live in or around that area and who may have private CCTV, or anybody who may have travelled along South Stack Road who may have dash cam footage.
"We are in the early stages of our investigation and are working hard to establish the circumstances behind this incident.
"A number of inquiries are under way involving detectives from CID, the local policing teams and Crime Scene Investigation.
"North West Wales remains one of the safest places in the UK.
"This is a highly unusual incident for this area and we are determined to find whoever was responsible for this as a matter of urgency."
Anybody who can assist the investigation should contact officers at Llangefni CID on 101 or via the live webchat quoting reference number X052857.
Contact can also be made with Crimestoppers anonymously via 0800 555 111.