Repeat offenders can see as many as six points subtracted in one go, though owners can earn points back with good behaviour such as volunteering in kennels.
Losing all 12 points means saying goodbye to the dog, the most severe punishment authorities can levy. Once a dog is confiscated, owners must pass an exam about responsible pet ownership before being reunited.
Since the programme was introduced last year, 1,430 dog owners had been fined, according to state media.
Of those, 122 lost the full dozen points, and subsequently their dogs; most, however, passed the exam and got their pets back. Local police say the number of complaints lodged about dogs has dropped significantly.
Other Chinese cities are now also beginning to roll out the dog owner social credit programme, reported state media.
"With proper implementation [of the system] and training, the overall quality of the dog owners will be raised," said Miss Hu, 35, a consultant in Beijing who owns a black Labrador retriever.
"It can reduce the risk of my dog being attacked by other dogs that are poorly kept," she said, declining to give her full name. The programme might also lower "the number of stray dogs and unleashed dogs, and eventually the number of people bitten by such dogs."
Dog bites have long been a concern in China, which has the world's second-highest number of reported rabies cases in the world, according to the World Health Organisation.
But that has not stopped millions of Chinese from owning dogs, leading to a boom in the pet care industry offering everything from doggie spas to pet funerals.
The dog-owner social credit system is similar to the government's nationwide social credit system launched in 2014.
The programme is being rolled out in phases, and is slated to be fully operational by 2020, though the government has provided scarce details about who is in charge of the system, how it works, and whether anyone can dispute the scores.
"By rating citizens on a range of behaviours from shopping habits to online speech, the government intends to manufacture a problem-free society," according to a Human Rights Watch report released in 2017.
- Additional reporting by Paula Jin
This article originally appeared on the Daily Telegraph.