Clermont Foot's president, Claude Michy, who initially said Costa's appointment as the club's coach was a "new era" in football, has said he was surprised by the decision.
"Helena Costa decided not to honour her commitments vis-à-vis Clermont Foot 63," said Michy. "Helena Costa will therefore not assume the role of club coach for the coming season. This decision was sudden and surprising.
"I deeply regret this situation. I thank all those who have supported me and I am most grateful. The operation of the club will continue with other stakeholders to prepare for the new season."
Costa, who is Portuguese, joined Benfica's academy as a teenager in 1997 and progressed from the Under-9s team to coaching the club's Under-17s, whom she led to two World Youth titles. Before being announced as the Clermont manager, Costa was most recently the coach of Iran's women's team and had been on the scouting staff at Parkhead.
Her appointment at Clermont created much media speculation as to how she would fare coaching men while others predicted it would begin a change in football's attitudes towards women.