Police said they were called at about 15:10 GMT to reports of a fallen tree at Bremhill near Calne.
When they arrived, they found a man in his 70s with serious injuries.
A spokesman said "early indications" showed the man was "electrocuted as he tried to clear the tree."  He was pronounced dead at the scene.
A Southern Electric Power Distribution spokesman said: "Earlier today we were, unfortunately, made aware of a fatality in the Melksham area.
"We were called to the site and made the situation safe and although we cannot speculate on the cause we can say the police were on site with our team.  We will continue to assist the police with their inquiries."
A man died in a suspected electrocution while trying to clear a tree that had brought down power cables in Wiltshire.