Scans identified an injury affecting a cervical facet joint, which plays an important role in maintaining stability and allowing movement in the neck. Despite the diagnosis, the 37-year-old is anticipated to be available when the four-match series begins in Perth on 9 December.
"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.
Smith was forced to miss Australia's deciding Test against South Africa in Cape Town after struggling with the problem for several days.
The discomfort first emerged during the second Test in Gqeberha, where he was moved down the batting order during Australia's unsuccessful attempt to save the match.
His condition deteriorated ahead of the third encounter, with the batter visibly uncomfortable during a nets session on the eve of the contest.
By the opening morning, his neck was heavily bandaged, and he was subsequently withdrawn from the playing XI as part of four changes to the Australian side.
Cameron Green returned from injury to replace Smith at number four, taking over the position normally occupied by the experienced batter.
The Proteas blew Australia's batting order away on the fifth day of the deciding Test at Newlands, the visitors crumbling to 111 all out as the hosts wrapped up a 176-run victory and a 2-1 series win.
Glenn Phillips struck a century while seamer Jacob Duffy took four wickets as New Zealand claimed a consolation victory in the T20I series against India in Auckland.
South Africa finished day three of the decisive third Test against Australia at Newlands with a narrow 40-run lead after a battling second-innings effort kept the hosts in the contest.
Australia took the upperhand on the second day of the third and deciding Test against the Proteas at Newlands after the tourists went to stumps on 330-4, a lead of one runs with six wickets remaining.
