The 37-year-old was ruled out of the third and deciding test against South Africa in Cape Town after battling a sore neck for a number of days.
Scans confirmed an injury to a cervical facet joint, which helps stabilise movement in the neck.
"Steve will continue to receive treatment and rehabilitation, with a full return to availability anticipated for the upcoming home test series against New Zealand," Cricket Australia said in a statement.
Team staff had hoped he could play at Newlands after batting in the nets on Sunday but ultimately deemed him unfit.
All-rounder Cameron Green returned from injury to bat in Smith's usual number four position in Cape Town.
Australia were 330 for four at the close of the second day in reply to South Africa's first innings 329.
Australia will host New Zealand in four tests, starting with the December 9 opener at Perth Stadium.