The arrest was made during a search operation at an address in Strabane this morning (26th May).
The man has been taken to the Serious Crime Suite at Musgrave Police Station where he will be questioned by detectives.
The arrest has been made after video footage emerged of an incident which shows a masked gunman firing shots into the air in a cemetery where a number of people are present and look on.
The PSNI statement adds that following enquiries, detectives believe the incident occurred in Strabane last month.