Coach Mike Holmgren said Friday during his radio program on Seattle's KIRO-AM that the season-ending procedure, performed Thursday, requires almost a 12-week recovery time.
"It should not be a major thing to affect him in training camp next year," Holmgren said.
Jones, 34, an eight-time Pro Bowl selection, had been playing in pain with the injury, which was aggravated before the Seahawks' Nov. 27 game at Dallas.
Earlier this week, he admitted looking forward to the 2009 season.
In 2007, his eighth Pro Bowl season, he started all 15 games in which he played.
The former first-round pick in the 1997 NFL draft out of Florida State has made 168 straight starts, a franchise record.