It is a shattering blow for the Australians, whose World Cup-strength bowling attack was flayed by New Zealand in last weekend's 3-0 Chappell-Hadlee Trophy series loss.
Stuart Clark, who was a controversial omission from the original 15-man squad named last week, is his replacement, pending International Cricket Council approval, CA said.
Australian team doctor Trefor James said following a review by an orthopaedic specialist it was decided that Lee's damaged left ankle ligaments would keep him out of cricket for two to three months.
Chairman of selectors Anddrew Hilditch said in a CA statement Friday that he had been advised that Lee's ankle injury was more serious than first expected.
Team medical staff in consultation with specialists advised that Lee will be unavailable for the World Cup, he said.
CA said it has written to the ICC's Technical Committee to receive approval for Lee to be replaced by Clark, in accordance with the relevant ICC rules.
"It is a great disappointment for Brett Lee that he is unable to take his place in the Cricket World Cup and is a significant blow for the planning and preparation in place for the tournament," Hilditch said in the CA statement.
"However it does give a tremendous opportunity for Stuart Clark to join the 15-man squad.
"Stuart was extremely unlucky to miss out on initial selection and despite the unfortunate circumstances surrounding his inclusion we strongly believe that Stuart is primed to seize his opportunity.
"Though Brett's injury is disappointing from a personal and team perspective, we strongly believe we are taking a squad of players more than capable of winning a third successive Cricket World Cup."
Cricket Australia General Manager Michael Brown said he had written to the ICC requesting a replacement player for Lee.
"Pending the ICC's advice on the replacement of Brett Lee, Stuart Clark is our nominated replacement in the squad of 15. I have today advised him that subject to ICC approval, I would expect him to be on the plane to the West Indies on Wednesday," Brown said.
Team doctor James said he had been advised that Lee's injury has not improved over the last week.
"On that basis I have advised Cricket Australia that Brett will not be fit to resume bowling for two to three months," James said in the statement.
Lee ranks behind Glenn McGrath and Shane Warne as Australia's third all-time leading wicket-taker in one-day internationals with 267 wickets in 150 matches.