Kevin Fleckney has been missing from his home in the Chirk Bank area of the town for more than 36 hours.
West Mercia Police has issued an appeal to help find the 56-year-old, who is listed as a high risk missing person.
People are being urged to call police on 101 with any information.
Oswestry Safer Neighbourhood Team (SNT) said: "We have concerns over the welfare of Kevin Fleckney, 56, missing for over 36 hours from his home in the Chirk Bank area of Oswestry.
"He is now listed with us as a high risk missing person. Any sightings 101 please."