No new dates for the rescheduled shows on their 14 on Fire tour were given in the statement announcing the postponement.
Promoters are asking for ticket holders to the shows, which was to include a single New Zealand concert at Mt Smart Stadium on April 5, to hold on to their tickets.
"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," the statement said.
Jagger, who arrived with his bandmates on Monday in Perth for the first leg of the Rolling Stones Australasian concert tour, was "completely shocked and devastated'' by L'Wren's death.
Jagger is expected to fly to New York to grieve with friends and family, although no official announcement has been made.
Ms Scott, 49, sent her assistant Brittany Penebre a text message at 8.30am on Monday (New York time), asking her to come to her ninth floor Chelsea apartment at 10am, but when Penebre arrived, she found the designer dead.
The New York Medical Examiner's Office will determine a cause of death, but the initial investigation points to Scott taking her own life, police sources said.
Her fashion empire was reportedly crumbling with a $US6 million (NZ$6.95 million) debt and last month she cancelled her London Fashion Week show at the last minute.
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