The procedure was carried out without complication in the player's native Australia on Wednesday after he was diagnosed last week.
Dragons coach Laurent Frayssinous said: "It's obviously a really bad news that affects the club in its entirety but we need to be united and strong and overcome that as a team. Scott must focus on his health and on his full recovery. We want to express our support to Scott and his family."
Former Newcastle Knights player Dureau, 26, is one of the most feared half-backs in Super League and scored 12 tries in 27 appearances in the competition last season.
- Sports & Recreation