He described the prime minister as his closest collaborator over a 30-year period.
Coulibaly, 61, had been chosen to run as the ruling party's candidate in this year's October presidential election.
He had only recently returned from a two-month stay in France where he had been undergoing health check-ups.
At the time, the government said that "after examinations on Monday 4 May at the Piti-Salptrire Hospital, he will take a few weeks rest, as prescribed by his doctor."
Coulibaly arrived back in the Ivory Coast on Thursday
On Twitter, President Ouattara said, "I salute the memory of a statesman, of great loyalty, devotion and love for the homeland. He embodied this young generation of Ivorian leaders of great skill and extreme loyalty to the Nation."
According to his official biography, Coulibaly leaves behind a wife and five children.
This is a developing story.