The France international sustained the injury after falling awkwardly during Arsenal’s 2-2 draw with Manchester City at Emirates Stadium.
Once the injury had an initial period to settle, an assessment with a specialist on Friday confirmed the need for an operation and the 29-year-old was treated straight away.
“He has had surgery and will be out for three months,” Wenger told Arsenal.com. “A reasonable delay is three months.
“It all went well, but it can be a week or two earlier or a week or two later, but it will be around three months.
“It is a blow of course, how big it will be we will only know afterwards because it will be down to how well we replace him. We bought [Calum] Chambers for that.”
Debuchy is often deployed in the right back position, but began his career playing as a midfielder usually acting as a deep-lying playmaker.
He spent nine-and-a-half seasons at Lille, including a Ligue 1 and Coupe de France double in 2010–11. He joined Newcastle United in January 2013, and was signed by Arsenal in July 2014.
Debuchy made his debut for the France national football team in 2011 and has since earned over 25 caps, playing at UEFA Euro 2012 and the 2014 FIFA World Cup.