Williams' withdrawal came less than 24 hours after losing in the final Auckland WTA tournament final.
"I don't believe she has an injury," Hobart tournament director Mark Handley said. "I just think that she's played a lot of tough, close matches over in Auckland and in the lead-up to a first Grand Slam (of the season) she's not taking any chances."
Williams was planning to use the Hobart event as final preparations for the Australian Open which begins Jan. 13. She lost in the third round at Melbourne Park last year.
The 33-year-old Williams lost 6-2 5-7, 6-4, to Ana Ivanovic at Auckland on Saturday. It was Williams' first final since winning her 44th career title at Luxembourg in October 2012.
The seven-time Grand Slam champion's ranking has fallen to 47th as she has battled injuries and Sjogren's syndrome, a fatigue-causing autoimmune disease, over the past two years.
Stephens first injured her wrist at the Hopman Cup team event on Friday and said scans might indicate she needed to take week off before the Australian Open.
"I was having some pain in my wrist and the doctor recommended I not play this week," the 12th-ranked Stephens said.
Gael Monfils also withdrew Sunday from the Heineken Open ATP event at Auckland, citing fatigue.
The Sydney International had its first upset Sunday when American Madison Keys beat seventh-seeded Simona Halep of Romania 6-1, 6-4. Third-seeded Sara Errani beat fellow Italian Roberta Vinci 6-4 6-2 another first-round match.
Agnieszka Radwanka of Poland is the No. 1 women's seed at Sydney and former Wimbledon champion Petra Kvitova is No. 2, and both have first-round byes.
Former No. 1 and sixth-seeded Caroline Woznicacki, playing her first match since becoming engaged to golfer Rory McIlory last week, faces a qualifer in the first round.
Juan Martin del Potro is No. 1 seed on the men's side and Jerzy Janowicz of Poland is No. 2, also both with first-round byes.
Defending champion Bernard Tomic, who won his first ATP title last year in Sydney before the rest of his season deteriorated into poor results on the court and some controversy off it, plays his first-round match Monday
Tomic, with new coach Velimir Zovko, takes on eighth-seeded Marcel Granolliers of Spain.
Zovko replaced Tomic's father, John, who is serving a one-year suspension from the ATP Tour for assaulting Bernard's former hitting partner last May.