Kaboul was missing from the 4-0 FA Cup defeat at Fulham after picking up the injury last week.
"Kaboul is having an operation on his knee," Redknapp said. "I'm not sure how long he'll be out for. Maybe six weeks."
Kaboul will miss both legs of Spurs' Champions League second-round tie with AC Milan and leaves Redknapp desperately short of cover at centre-back.
Michael Dawson was sent off at Craven Cottage and will serve a three-match suspension, William Gallas has a hip niggle and Jonathan Woodgate and Ledley King are both some way off full fitness thanks to long-standing groin injuries.
Centre half Bongani Khumalo, a ?1.5million signing from South African side Supersport, and versatile full-back Vedran Corluka may now be forced into action over the next few weeks.
Source: PA
Source: PA