Dupont limped off in the first half of France's 42-27 victory over Ireland on Saturday after his knee buckled under pressure from the Irish defence at the back of a ruck.
"My heart hurts even more than my knee when I have to abandon my friends before the last step," Dupont wrote in a post on social media.
"I'm proud of what we achieved yesterday and with all my strength with you, you're going to do it. Cruciate ligament rupture. This is the start of a new challenge, and I look forward to seeing you on the pitch in a few months' time."
France moved to 16 points, two ahead of Ireland and six clear of England, and any win over Scotland will almost certainly help them secure the title, given their far superior points difference.
Coach Fabien Galthie said France had recommended that the two Irish defenders who made contact with Dupont - Tadhg Beirne and Andrew Porter - should appear before the disciplinary commission.
Dupont looks likely to miss the rest of the season, which is due to end in June. His club Toulouse lead the French Top 14 standings with 46 points after 13 games, one ahead of Bordeaux Begles.