The 45-year-old was hospitalised with a swollen left calf on Saturday, prompting Cricket Australia (CA) to put batting coach Michael Di Venuto in charge for the three-match Twenty20 series against India starting at Adelaide on Tuesday.
"Darren is in good health and feeling well at the moment but is still awaiting medical clearance for us to be satisfied that it is safe for him to fly," CA chief medical officer John Orchard said in a statement.
"As such, he will not travel to New Zealand for the one-day international series. He is meeting with specialists in Sydney later this week and will have repeat scans on Friday to check his progress."
CA has not named a replacement for the three-match ODI series in New Zealand starting on February 3 but expects Lehmann to be back in charge for the subsequent two-match Test series.
"We have strong depth in our coaching ranks and will make that decision in due course," CA executive general manager of team performance Pat Howard said.
"It is anticipated that Darren will make it back for the Test series but as with all the decisions we make, we will be guided by medical advice."
Image: Australia coach Darren Lehmann during a training session.
Photograph: Philip Brown/Reuters
Australia's Lehmann to miss T20 series against India
Cricket Australia to address imbalance between bat and ball
Khaleel, Sarfaraz shine as India thrash Pakistan in U-19 WC warm-up
'We want to get a bit of momentum in the T20s against India'
Injured Maxwell to miss T20 opener vs India