Tomljanovic won the first set against Tauson in a tiebreak, 7-6 (7-5), on Monday's opening day of the WTA 500 tournament.
Tauson, who played with a vertical bandage on her left hamstring, followingly sought medical treatment before she tearfully chose to retire, and the cause of her decision isn't known at this stage.
Tauson was seen speaking to the physio and moments later, Tauson shook hands with the chair umpire and Tomljanovic, as the match ended prematurely.
Clara Tauson, who is number 14 in the world rankings, has had a dreadful start to the season after losing her first match in Brisbane last week.
Adelaide was the 23-year-old Dane's last warm-up tournament before Australian Open in Melbourne later in January.
In October last year, Tauson had to withdraw from her last WTA tournament of the season in Hong Kong with an injury and she subsequently also withdrew from the Billie Jean King Cup in November.
At that time it was said that she was rehabilitating after "physical problems", but she was not fit enough to play matches. It now remains to be seen whether she will be able to regain full fitness in time for the first grand slam tournament of the year.