"Jacques is undergoing ongoing treatment but it's a week-by-week thing. I'm confident though that he will be fit for the World Cup," team doctor Mohamed Moosajee told a news conference on Tuesday.
Kallis's presence will bolster a South African batting line-up, which has struggled in the last two matches against India. The 35-year-old all-rounder is also a top-class seam bowler, allowing the team to play a specialist batsman at seven.
Wicketkeeper-batsman Morne van Wyk, who smashed South Africa's quickest Twenty20 [ Images ] half-century two weeks ago, is the only other player named who was not part of the squad for the first three One-day Internationals against India.
Twenty-one-year-old batsman David Miller, who played in the first two ODIs against India, was left out of the squad for the tournament on the sub-continent, which starts next month.
Veteran wicketkeeper Mark Boucher [ Images ], who is still a senior member of the Test team, was also a controversial omission, although his last limited-overs international was in the West Indies [ Images ] in June.
South Africa's middle-order problems meant Faf du Plessis, who scored a defiant 60 on Tuesday on his ODI debut, was preferred to Miller.
Imran Tahir, the Pakistan-born leg-spinner who has been in marvellous form in domestic cricket, was included although he is yet to play in the current series.
"We think Tahir is a unique talent but it has been difficult for him to play in this series because it is difficult to play two spinners in South African conditions, but we hope to start him soon," convenor of selectors Andrew Hudson said.
South Africa are trying to improve a miserable record at World Cups, where they have usually been among the favourites but have never progressed beyond the semi-finals, often finding bizarre ways of exiting cricket's premier one-day tournament.
They will play India, England [ Images ], West Indies, Bangladesh, Ireland and the Netherlands in Group B.
Squad: Graeme Smith, Hashim Amla [ Images ], Jacques Kallis, AB de Villiers, JP Duminy [ Images ], Faf du Plessis, Colin Ingram, Johan Botha [ Images ], Wayne Parnell [ Images ], Dale Steyn [ Images ], Morne Morkel [ Images ], Robin Peterson, Imran Tahir, Lonwabo Tsotsobe, Morne van Wyk.