Mr Cowie has represented Buckie as an independent councillor since winning a by-election in January 2014, but feels the abuse has become too much for him to carry on.
Although his age is a factor in not choosing to stand again, he says the main reason for his decision is the increasing anger shown verbally, online and in hate mail.
‘Threatening and abusive communication’ reported to police
A spokesman for Police Scotland said: “We have received a report of threatening and abusive communication in the Buckie area.
“Inquiries are currently ongoing.”
With nominations for the local council elections announced last week, Buckie is the only ward of the eight in Moray where a ballot will not be held.
Three people put themselves forward, Conservative Neil McLennan, Liberal Democrat Christopher Price and Sonya Warren for the SNP.
They will all be declared councillors without a vote being cast for them.
Police confirm investigation into hate mail sent to Buckie councillor