Association chairman Gareth Baines said: "The overwhelming vote of no confidence by ordinary Conservative grass roots members in Clwyd South should send a clear and unequivocal message to Theresa May: go now.
"Whilst Clwyd South may have been the first association nationwide to hold such a vote, I’ve been inundated with contact from other associations who now seek to follow our lead."
He added: "Coupled with polling from Conservative Home, which shows Mrs May to be the least popular Prime Minister ever, it’s clear the overwhelming majority wish for Mrs May to stand down before she does anymore damage to the country, or to the party.
"Yesterday’s vote was preceded by an open and amicable debate, where various issues regarding Mrs May’s leadership were aired, mostly around things not related to Brexit.
"It is clear, through her own actions, Mrs May has lost the support and goodwill of grass roots Conservatives in Clwyd South and across the country."