Lee took an early flight home to see a Sydney specialist after he fell awkwardly during training on Thursday in Wellington.
Australian team physiotherapist Alex Kountouris said the decision was made after scans were taken at Wellington hospital.
The scans will reveal the extent of ligament damage suffered when Lee wrenched his ankle while sliding to stop a ball.
The loss of Lee further depletes the Australian side which is without captain Ricky Ponting and wicketkeeper Adam Gilchrist, who are being rested, as well as the injured Andrew Symonds. Batsman Michael Clarke is also set home with a hip problem.
South Australian fast bowler Shaun Tait has been called in to replace Lee for the three-match Chappell-Hadlee series which starts here Friday.