Tomic, once dubbed "Tomic the Tank Engine" in his native Australia after being accused of giving up in a match, was 6-3 3-0 down to Teymuraz Gabashvili when he told officials he was unable to continue.
Rain prevented any matches being completed on Thursday so Tomic, if he had beaten the Russian, would have had to play a semi-final later on Friday, as well as potentially Saturday's final, before taking on Denis Istomin at the Australian Open.
Tomic later told reporters he had been feeling a "bit sick" on Thursday evening and a conversation with the umpire picked up by the on-court microphones during a break in play in the first set showed where his priorities lay.
"I got a good draw in Melbourne, it's just come out, I'm looking to Melbourne," said the world number 17, adding that even if he won the title in Sydney he would move up only one spot in the rankings.
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"I have to make the final to make (rankings) points, I have to win to go 16th in the world," said Tomic, who won his first ATP title in Sydney in 2013.
Gabashvili will play Viktor Troicki in his first ATP Tour semi-final later on Friday after the Serbian defending champion came from a set down to beat Nicolas Mahut 4-6 6-3 6-3.
Grigor Dimitrov, continuing his promising start to the new season, will face Gilles Muller of Luxembourg in the other last four contest at Olympic Park.
The Bulgarian was leading his quarter-final against Alexandr Dolgopolov 4-6 6-3 4-2 when it was interrupted by a violent thunderstorm on Thursday.
The 24-year-old wasted little time in wrapping up the final set 6-4 with an ace on his first match point on Friday, however, despite the uncertainties caused by the weather.
"It's tough, we were on and off the court four times yesterday but it's in the game," Dimitrov said.
Muller was the first player to advance to the semi-finals when he completed a 7-6(5) 6-3 win over Frenchman Jeremy Chardy in another match interrupted on Thursday.
(Editing by Peter Rutherford)
