Critics say China's late-1970s family-planning law, which restricts most couples to one child, is selectively and sometimes brutally enforced, while the wealthy and well-connected are easily able to pay the fines levied for extra offspring.
But in recent days some users of China's popular online social networks have directed their anger at the policy itself, rather than Zhang, with some hoping the attention heaped on his case may hasten the eventual demise of the law, which authorities have recently moved to relax.
Two lawyers filed a lawsuit on Thursday in the eastern city of Wuxi, the hometown of Zhang's wife, suing the director of "Red Sorghum" and "Raise the Red Lantern" for a total of one billion yuan ($164 million), the government-run China Daily said in a front-page report.
"The rich have become increasingly audacious by violating the family planning policy just because they are rich enough to pay the fine... and they take an extra share of resources from society," it quoted one of the lawyers, Jia Fangyi.
"It's unfair to the poor and those who strictly follow the national policy," he added in a statement.
The two lawyers are claiming 500 million yuan in "compensation for public resources" and another 500 million yuan in punitive damages, the China Daily said, adding that the court might not accept the case.
Zhang, one of China's best-known filmmakers and the director of the opening and closing ceremonies at the 2008 Beijing Olympics, had faced rumours for months that he had fathered as many as seven children with several different women.
Amid increasing pressure -- including a Nanjing newspaper's publication last month of a front-page "wanted" poster seeking information on his whereabouts -- Zhang finally issued an apology on Sunday through his studio's microblogging account.
He acknowledged that he has two sons and a daughter with his current wife, as well as another daughter with his ex-wife.
The one-child policy was put in place to control China's booming population, and officials say it has been key to the country's rising prosperity.
But opposition to it has steadily grown among members of the public as well as among demographic experts, who warn that it has led to a decline in China's working-age population and a swelling of the ranks of the elderly that could bring about a labour shortage within the next two decades.
Those fears appear to be shared by China's Communist Party leaders, who after a key meeting in Beijing last month moved to expand the exceptions to the policy to allow couples to have two children if one of the parents is an only child.
In the past Chinese web users have typically responded with fury to reports of celebrities escaping the one-child regulation, but sentiments over the past week have been more mixed, with some citing Zhang as an example of why the law should be scrapped.
"We should be grateful to Zhang Yimou!" one posted on Sina Weibo, a Chinese equivalent of Twitter. "Thanks to his popularity, he's made the whole society debate the problems of the 'family planning policy'! This might help speed up the abolition of this draconian law."
Another said the controversy was "more than ridiculous", adding: "Procreating is a fundamental human instinct and a way of passing things on to future generations. Here in China, it's actually become a crime."
Chinese media reports have speculated that Zhang could face an official penalty as high as 160 million yuan, but authorities have not released any figures.
Fines for violators of the one-child policy are a significant source of income for China's provincial governments.
In 2012, 24 of the country's 31 provinces and regions collected a total of nearly 20 billion yuan ($3.3 billion) in penalties, the Beijing News reported on Thursday. None of the provincial authorities has detailed how the money was spent.