The body of the 60-year-old man was discovered in the Aghindarragh Road area in Augher on Friday evening.
Police have confirmed they are treating the death as suspicious.
The 18-year-old man remains in custody.
Local Ulster Unionist MLA Tom Elliott described the death as a tragedy.
"While the police are obviously investigating the circumstances around this death it is clearly a very difficult time for the family and wider community.
"I trust the police can develop their investigations at an early stage and establish the facts of the case," he added.
"Augher is a close knit rural community where an incident like this will have a bearing on the general population of the area."