He also said on Monday he was considering his playing future in the wake of his non-selection.
Selection convenor Joubert Strydom said Kallis was being rested for the tournament, which will be played in South Africa in September, but the all-rounder said he was disappointed to be out.
"I have resigned as vice-captain and I'm considering my options with regard to the rest of my career," Kallis told reporters.
"I have been thinking long and hard over the weekend and there is still a lot of emotion involved because I am extremely disappointed. I was very excited about the tournament and hoping to make a huge contribution."
Kallis, 31, has been South Africa's outstanding player of the past decade but at times he has been criticised for slow batting.
He has played in 107 Tests and 261 one-day internationals and is the only man in world cricket to have scored 8000 runs and take 200 wickets in both forms of the game, but at times he has been criticised for slow batting.
However, the 31-year-old believed he still had much to offer as a player.
"I feel I have a lot of good cricket and my best years might even be ahead of me," he said.
"Ideally I would like to play many more years for my country but this weekend caused me to question my future for the first time," added Kallis, who has played 107 tests and 261 one-day internationals.
CSA urge Kallis to withdraw resignation: Meanwhile South African cricket(CSA) authorities said it hoped star all-rounder Jacques Kallis would withdraw his resignation as vice-captain of the national team, reports AFP from Joburg.
Cricket South Africa (CSA) chief executive Gerald Majola said in a statement that Kallis had telephoned him Monday to say he was resigning as vice-captain.
"I said we all understood his disappointment, and appealed to him not to resign while in an emotional state but to rather meet with CSA to discuss the matter fully so that we could deal with all the issues at hand.
"It is most disappointing therefore that Jacques took a unilateral decision after speaking to me to publicly announce his resignation as vice-captain."
Majola said Kallis's actions were regrettable in view of a recent agreement between CSA and the South African Cricketers' Association which outlined the way issues involving players should be dealt with.
"Jacques is employed by CSA, and we expected him at least to sit down at a meeting and go through the matter before he made his own decision to make a public announcement.
"The reasons for his omission from the squad were fully explained to him as well as the prominent role he will play in a very full and varied season after the tournament.
"CSA hopes that Jacques will reconsider his decision because we believe that he has much to offer as vice-captain and has been a stalwart on the field for South African cricket for more than a decade.
"I do not want to get into a public debate on this issue, and will seek again a meeting with Jacques to discuss the matter fully with him and will ask him to reconsider his decision to resign as vice-captain," said Majola.