In a press release, the Blues revealed Judd "is expected to resume full training in January" and the operation should take place early next week.
Judd had precautionary scans on his shoulder Wednesday after experiencing some discomfort during pre-season training.
"After a meeting with his specialist it was decided he would undergo a minor procedure to ensure he is ready for the start of the 2012 season," the statement said.
"Chris will have a minor procedure on his shoulder early next week," general manager of football operations Andrew McKay said.
"At this time of the year it is best to ensure he commences 2012 in peak condition and being a shoulder injury he will be able to maintain his fitness before resuming full training in January.
"Thankfully this injury will have no impact on his 2012 season."
Earlier, coach Brett Ratten refused to speculate on the injury on SEN Radio.
Ratten said he was unsure how the injury occurred but suspected it happened during marking practice.
A website part-owned by Judd's manager, Paul Connors, was reporting that the skipper could miss up to four months after a full shoulder reconstruction.
Judd, 28, is believed to have trained as recently as Tuesday and The Age reports the injury is a result of a relatively innocuous "training mishap". He started his pre-season on Monday, missing the team's recent training camp in Qatar and Abu Dhabi.
Judd has a history of shoulder injuries and had surgery twice as a junior footballer. His shoulders were the reason he slipped from No. 1 draft pick to No. 3 in the 2001 draft.
However, he has avoided major shoulder surgery in his 10-year career, despite always playing with heavily strapped shoulders.
