The 32-year-old fullback collapsed in a goalmouth near the end of the first half of Al Wakrah's match against Al Rayyan at Doha's Al Gharafa Stadium and was treated by medical and ambulance staff on the pitch.
"Thank you for your messages of support and love, Ousmane is in stable condition due to his heart attack, he regains consciousness slowly but surely," his wife posted on his Instagram account.
"He is in very good hands. Al hamdoulilah. Many thanks to God and the doctor who saved my husband's life! Thank you for all the staff and the team of Al Wakrah SC.
"I appreciate all you did for us. Let's continue to pray."
Coulibaly was born in Paris and played for French clubs Guincamp and Brest before spells with Platanias and Panathinaikos in the Greek Superleague.
He joined Al Wakrah in 2019.
"The Qatar Stars League wishes the player a fast recovery, and we would like to thank the medical staff of both teams, paramedics and doctors for their great efforts during such events," the league said in a statement.
The match, which was abandoned with Al Rayyan winning 1-0, will be completed on Monday at a different stadium. Coulibaly is not the first professional footballer to suffer a heart attack on the pitch. Danish forward Christian Eriksen suffered a cardiac arrest on the pitch during a European Championship match against Finland in Copenhagen in June last year. The 29-year-old was fitted with a heart-starting device. His contract with Inter Milan was terminated on medical grounds but he is looking for a new club to continue his career.