The former Inter coach is in hospital for tests after breaking down following the 1-0 win over Olympique Lyonnais at Stade Gerland on Sunday
The Brazilian was rushed to hospital in the French capital on Monday to undergo tests on the fall, and it is believed that he had a blood pressure problem.
As a result of his collapse, the former AC Milan and Inter coach did not participate in PSG's bus parade through the city of Paris.
Club president Nasser Al-Khelaifi told reporters: "Leonardo give his heart and his health for the club."
Carlo Ancelotti's side claimed a 1-0 win over Olympique Lyonnais on Sunday to clinch their title, their first since 1994, having led Ligue 1 for much of the season.
Jeremy Menez scored the decisive goal just after the break at Stade Gerland.