The two concerts in Shanghai and Beijing were to have been the British group's first in the world's most populous nation, despite their regular applications for permission to play there since the 1970s.
The long-delayed shows had originally been scheduled for earlier this year but were cancelled due to the Severe Acute Respiratory Syndrome (SARS) epidemic that ravaged the country and had been rescheduled for November.
"The Stones had hoped to reschedule at this time, but the details for reorganising the dates proved far more complicated and difficult than expected," their New York-based publicist said in a statement in Los Angeles.
No alternative dates
"The band looks forward to playing concerts in these cities in the future," the statement said. No possible alternative dates were given for the mainland Chinese concerts.
But the Stones said planned concerts in Hong Kong, their first in the former British territory in 40 years, would go ahead on 7 and 9 November despite the on-off plans that have plagued those shows.
In September, Chinese promoters said final preparations were being made to mount the two shows in the communist country's main cities in November, despite the fact that the contracts had not been finalised.
"The details for reorganising the dates proved far more complicated and difficult than expected"
Rolling Stones, New York
The Beijing show was to have taken place in the 18,000-seat Capital Gym.
The band had originally been scheduled to perform in Shanghai on 1 April and Beijing on 4 April as part of their Forty Licks world tour but the SARS crisis forced them to cancel.
The group, fronted by Mick Jagger, have made clear that after decades of trying to mount shows in China, the country is high on their list of priorities.
Beijing's stringent Ministry of Culture once viewed rock music as "spiritual pollution," but finally caved in and approved the concerts in early February.
The Hong Kong shows are part of an effort to revive the territory's spirits after the devastating SARS epidemic that was centred in China and Hong Kong.