The 24-year-old Dane, who lost the final of the Auckland Classic on Saturday, had already had her left wrist strapped when she was forced to retire at 6-4 1-1 down to Czech Barbora Zahlavova Strycova.
"I didn't want to do it worse before Melbourne, so I'm just going to try and get some treatment on it and try and get ready for next week," Wozniacki told reporters.
"I still have a week to go, so hopefully it'll be fine... I'm confident that I'll be fine to play in Melbourne."
Zahlavova Strycova went through to a second round tie against local hope Sam Stosur, who had earlier progressed with a rain-disrupted 7-6(3) 5-7 6-3 victory over another Czech in Lucie Safarova.
Former U.S. Open champion Stosur had already had her first-round contest put back a day after wet weather in Sydney on Sunday.
She held her nerve throughout a three-hour contest peppered with rain interruptions and polished off the victory over the world number 16 with a thumping ace down the middle.
It was a welcome return to winning ways for Stosur, who blew a 5-1 lead in the third set last week to lose to American Varvara Lepchenko in Brisbane.
"I was pleased with the way I served for the match," she said. "After what happened last week, to step up and serve the way I did, I'm obviously very happy."
Third seeded Pole Agnieszka Radwanska enjoyed the more clement later conditions to beat France's Alize Cornet 6-3 6-2 and reach the second round of a tournament she won in 2013.
The world number five made it clear, however, that her focus over the next few weeks under new coach Martina Navratilova was on improving on a single semi-final appearance at Melbourne Park.
"Martina's going to be here tomorrow," Radwanska said. "She's really helping me on and off court. The goal is the grand slams so we'll see how it goes."
In the men's draw, fifth-seeded Argentine Leonardo Mayer downed Benjamin Becker 7-6(3) 6-2 to set up a meeting with young Australian Nick Kyrgios or Pole Jerzy Janowicz in the second round.
Local top seed Casey Dellacqua overcame a second-set glitch to beat American Lauren Davis 6-4 1-6 6-4 and reach the second round of the Hobart International.
(Editing by Sudipto Ganguly)
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