The fashion designer was found dead inside her Manhattan apartment Monday morning, an apparent suicide. She was 49.
"The Rolling Stones are deeply sorry and disappointed to announce the postponement of the rest of their 14 ON FIRE tour of Australia and New Zealand following the death of L’Wren Scott," show promoters announced Tuesday.
"Mick Jagger, Keith Richards, Charlie Watts and Ronnie Wood wish to thank all of their fans for their support at this difficult time and hope that they will fully understand the reason for this announcement."
Ticket holders are asked to hold on to their tickets until a new schedule is worked out. "Information will be made available via rollingstones.com and frontiertouring.com as soon as available," said the notice.
Jagger, 70, began dating Scott in 2001. On Monday night, the singer's rep issued a statement refuting a report that the rock legend had recently ended his relationship with her.
"The story in the New York Post re a split between Mick Jagger and L'Wren Scott is 100% untrue," said his spokeswoman, Victoria Scarfone. "There is absolutely no basis in fact to this story. It is a horrible and inaccurate piece of gossip during this very tragic time for Mick."
Jagger also, on Tuesday, posted a touching tribute to Scott on Facebook.
Scott dressed A-list stars like Nicole Kidman, Sarah Jessica Parker and Olivia Wilde in her gowns.
The BBC also reports that according to its last U.K. filing, Scott's firm, LS Fashion Limited, owed creditors about $7.6 million as of the end of last year, on assets of $1.7 million.
Raised in Utah as Luann Bambrough, Scott reinvented herself as a model in Paris and later became a stylist to the stars in the '90s, according to a 2009 Daily Beast interview.