Schiavone, the 2010 French Open champion, was bundled out by Lucie Safarova 6-4 6-4. The 33-year-old Italian was also knocked out of the first round of the Brisbane tournament last week by former world number one Jelena Jankovic.
Serbia's Jankovic, the fourth seed in Sydney, is due to face Russia's Ekaterina Makarova on the main Ken Rosewall Arena court later on Monday, while Denmark's Caroline Wozniacki will face Germany's Julia Goerges.
Australia's Samantha Stosur's bid to ensure she was not the third grand slam champion to leave a tournament in the first round on Monday was proving a struggle against American Madison Brengle at the Hobart International.
Rain had disrupted play in Tasmania with Stosur and qualifier Brengle forced off court for more than two hours with the Australian holding a 2-1 lead in the first set.
The 23-year-old Brengle, however, took advantage of the break to regroup and raced to a 6-5 lead in the first set to place the top seed under immense pressure before rain again forced them from the court.
WRIST INJURY
Stosur, the 2011 U.S. Open champion, has not advanced beyond the fourth round at home in the past five years, with six first round exits in 14 tournaments in Sydney, Brisbane and the Australian Open.
She lost all three of her matches in the Hopman Cup in Perth before entering Hobart, which had attracted a strong field before a rash of late withdrawals.
Fifth seed Flavia Pennetta was the latest withdrawal from the tournament on Monday with a wrist injury, following seven-times grand slam champion Venus Williams, who pulled out on Sunday.
Pennetta had been due to face Williams in the first round.
"Unfortunately I felt some pain in my wrist in Perth and it hasn't had time to recover so sadly I have to withdraw," Pennetta said.
The 33-year-old Williams was beaten in the final of the Auckland Classic by Ana Ivanovic on Saturday and said she could not have withstood another tournament so went directly to Melbourne to prepare for the season-opening grand slam.
Champion Elena Vesnina, who arrived in Hobart last week to prepare for her title defence, is scheduled to play Puerto Rico's Monica Puig later on Monday.
(Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien)
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