The designer, whose company was heavily in debt, was found dead in her New York apartment Monday in an apparent suicide.
Concert organizer Frontier Touring said Tuesday that a Stones show scheduled for Wednesday in Perth, Western Australia, would not go ahead. There was no immediate word on future dates on the tour, including a Saturday concert in Adelaide.
The Stones are scheduled to tour Australian and New Zealand, then play a string of European dates starting in June.
Scott was found dead in her Manhattan apartment at 10 a.m. Monday by an assistant; police said no note was found and there was no sign of foul play. Scott was found kneeling with a scarf wrapped around her neck that had been tied to the handle of a French door, police said.
Jagger's representative said the singer was "completely shocked and devastated by the news" of Scott's death.
Last month Scott, who was believed to be 49 but had not disclosed her precise age, canceled her London Fashion Week show, due to reported production delays.
Accounts filed by Scott's LS Fashion Ltd. in London show the company had liabilities that exceeded assets by 4.24 million euros ($5.9 million) as of Dec. 31, 2012.
The company's long and short-term debts totaled 6.75 million euros against assets, capital and reserves of 2.51 million euros, according to the accounts, which were filed in October.
Scott was adopted by a Mormon couple and grew up in the small town of Roy, Utah. As a teenager, she developed a love of clothes and made her own, according to biographical notes from London Fashion Week. She made her way to Paris after high school where, aided by her 6-foot-3 (1.9 meter) height and striking looks, she found work as a model for some prominent photographers.
But she became more interested in working with clothes than modeling them, and eventually made her name as a top stylist in Los Angeles and a costume designer for films including "Ocean's 13."
Scott, whose elegant designs in lush fabrics were worn by celebrities including Madonna, Nicole Kidman, Oprah Winfrey, Penelope Cruz and U.S. first lady Michelle Obama, had been a fixture on Jagger's arm since she met the Rolling Stones frontman in 2001. On red carpets, the designer towered over her famous boyfriend.
In 2006, Scott founded her eponymous label, with an initial collection based on the "Little Black Dress." She became known for designs that had a vintage feel and bared little skin, such as her famous "headmistress" dress - prim, with three-quarter sleeves, but also close-fitting and stylish.
Madonna was one of those who wore Scott's designs and called her death "a horrible and tragic loss."
"I'm so upset. I loved L'Wren's work and she was always so generous with me," the singer said in a statement released by her publicist.
Vogue editor-in-chief Anna Wintour called Scott "a total perfectionist, someone who absolutely embodied everything her marvelous clothes stood for: strength of character combined with a confident and powerful style."
And supermodel Naomi Campbell, a close friend, wrote on WhoSay that Scott was "the epitome of elegance and femininity yet still had a girlish quality. I will miss her honesty and I will miss her friendship. My heart goes out to Mick and all who loved her and were loved by her."
Associated Press Writer Danica Kirka in London contributed to this report.