"On that basis I have advised Cricket Australia that Brett will not be fit to resume bowling for two to three months," James said.
Andrew Hilditch, Australia's chairman of selectors, has written to the International Cricket Council asking for Stuart Clark to replace Lee in the squad.
"It is a great disappointment for Brett Lee that he is unable to take part in a Cricket World Cup and is a significant blow for the planning and preparation in place for the tournament," Hilditch said in a statement.
Stuart Clark said his selection was tinged with sadness: "It's really disappointing for Brett. It's hollow, but I'm still excited about going to the World Cup."
Lee is Australia's main strike bowler and his withdrawal is a big blow to the team's chances of winning the World Cup for a third time in a row.
The world champions have lost their last five matches - their longest losing streak in a decade - and surrendered the world number one ranking to South Africa.
They were white-washed by New Zealand in the Chappell-Hadlee trophy and beaten 2-0 by England in the final of the Commonwealth Bank series; that despite being dominant during the preliminary matches.
The baggy greens are also facing a mounting injury list, with captain Ricky Ponting, wicket-keeper Adam Gilchrist, all-rounder Andrew Symonds and batsmen Michael Clarke and Matthew Hayden all out of action at the moment.