The event was scheduled for February to coincide with the start of the Chinese lunar year of the dog, and a poster advertising it showed poodles with dyed pink fur clapping their paws and doing handstands.
However the show, reportedly from China and set to include acrobatics and clown acts, came under fire online and a petition was started on website Change.org.
The petition, which quickly garnered over 7,000 signatures, branded using animals in circuses as "archaic, cruel, and unethical" and called for an "end to the inhumane and outdated practice".
"The Chinese New Year Dog Circus 2018 show has been cancelled," it said in a Facebook post, adding ticket sales had been stopped.
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The show was due to take place at Resorts World Sentosa, a resort on an island off Singapore, but was being put on by an outside production company.
Louis Ng, a lawmaker and founder of ACRES, a local animal welfare group, told AFP he hoped organisers would "get the message that using animals for entertainment is something outdated and it's not something that Singaporeans want."