Kallis will have an operation to repair tendinitis in his left elbow that has troubled him since November.
A CSA media release said Kallis was ''unlikely'' to recover from the operation in time to be considered for the tour.
''He should be fit and ready for the Champions Trophy in India in September and the 2007 World Cup in West Indies in March,'' the release quoted the South African team's physiotherapist, Shane Jabaar, as saying.
''The decision to undergo surgery to his left elbow has been taken against a background of chronic pain and inflammation through what is commonly known as a tennis elbow.
''Jacques will undergo a one-hour operation on a tendon in his elbow next Wednesday, and will be out of the clinic the same day.
''He will be in splints for 10 to 12 days and will then start his rehabilitation over a period of four to six weeks.'' South Africa will play three tests in Sri Lanka and the squad will be named in June.