A rift has developed among the top executives of three of China’s internet giants, in the wake of Didi Global Inc.’s ill-fated decision to go public in New York.

Didi’s eight-member board of directors—which includes leaders of Tencent Holdings Ltd. and Alibaba Group Holding Ltd. —approved the ride-hailing company’s plan to push through with a $4.4 billion U.S. initial public offering in June, even though the country’s cybersecurity watchdog had suggested to Didi that it postpone its share sale.

After the listing, Tencent President Martin Lau and Alibaba Chairman and Chief Executive Daniel Zhang were surprised and furious when they learned that Didi was in trouble with the Cyberspace Administration of China, according to people familiar with the matter. Tencent and Alibaba are longtime shareholders of Didi.

Two of the people said Didi executives didn’t fully inform the board about the the cyberspace regulator’s concerns prior to the IPO, making it hard for board members to fully ascertain the risks of going ahead.

Since early July, Beijing-based Didi has been subject to a series of punitive actions by Chinese regulators that have sent its newly listed shares plunging. The Chinese government has restricted Didi from accepting new users in the country, removed dozens of its apps from domestic app stores and put it under investigation by seven ministries.

Didi had received mixed signals from different government agencies prior to the IPO and some other regulators had been supportive of its listing plans, The Wall Street Journal reported previously. China currently has no rules that require internet companies to obtain Chinese government approval for overseas listings; its regulators are in the process of changing that.

Messrs Lau and Zhang had earlier advised Didi Chairman Will Cheng and President Jean Liu —who also sit on the eight-member board—against rushing to go public in the midst of China’s wide-ranging regulatory crackdown on the business practices of dozens of internet-technology companies, the people familiar with the matter said. The South China Morning Post earlier reported that the Tencent and Alibaba executives advised Didi to defer its New York listing.

The fallout from Didi’s IPO—and China’s intensifying regulatory crackdown on internet-technology and other businesses—has rippled across companies and Chinese stocks listed on multiple exchanges. Many Chinese tech startups have been forced to reconsider their overseas IPO plans and global investors have become less eager to invest in companies from China.

Days after Didi’s listing, China said it would tighten rules for companies seeking to sell shares abroad. A draft regulation requires tech companies with data from more than one million users to undergo cybersecurity reviews before pursuing foreign listings.

Alibaba and Tencent are facing their own regulatory issues and can ill afford further entanglements with Didi’s problems. In April, Alibaba was slapped with a record $2.8 billion fine for anticompetitive behavior on its e-commerce marketplace. Various Tencent subsidiaries have also faced punitive actions, although the company as a whole hasn’t been the subject of major regulatory scrutiny. Shares of both companies have tumbled this year.

Before Didi’s IPO, China’s cyberspace regulator suggested that the company postpone its share sale until it completed a data-security review, meant in part to ensure that private data from Didi’s users wouldn’t be shared outside the country.

It isn’t known how much detail Didi executives shared with the company’s board. Didi’s IPO prospectus made several references to data security, but didn’t mention the cyberspace administration’s request for a review.

“The board is a venue to make strategic decisions and an IPO is a strategic decision. It would be unusual if the management has not discussed that in detail or has not passed on the guidance from a regulator for an IPO at the board,” said Jamie Allen, secretary-general of the Asia Corporate Governance Association in Hong Kong.

Didi signaled to the cyberspace regulator that it would consider the request, but at the same time pressed ahead with the IPO. The company went public on the New York Stock Exchange on June 30—the eve of the Communist Party’s centennial celebration—in a low-key manner, with no bell-ringing ceremony and little publicity.

After drawing Beijing’s ire, Didi has been criticized in China by government officials, investors and entrepreneurs, who have called it two-faced.

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After Chinese ride-hailing giant Didi made its Wall Street debut, Beijing said it plans to tighten rules for homegrown companies looking to raise money overseas. WSJ’s Yoko Kubota takes a Didi ride to explain what the crackdown means for China’s tech titans and investors. Photo illustration: Ang Li The Wall Street Journal Interactive Edition

Mr. Cheng, an Alibaba alumnus, started Didi in 2012 after a six-year stint at the e-commerce giant, which is based in Hangzhou. He couldn’t obtain funding from his former employer because then-Chairman Jack Ma informally banned investing in startups founded by alumni, according to people familiar with the matter.

The informal ban, designed to help Alibaba keep talent from leaving to start other companies, was later scrapped partly because Mr. Ma regretted missing out on Didi, the people said.

Filling the void, Tencent became one of Didi’s earliest and most important backers. The social media and gaming giant first invested $15 million in the company in 2013 and pitched in on several more fundraising rounds in the ensuing years, according to PitchBook data. Tencent owned 6.8% of Didi at the time of its IPO.

Alibaba backed Didi’s former rival, Kuaidi. When Didi and Kuaidi engaged in a costly battle for market share in China between 2013 and 2015, their competition also fueled tensions between Tencent and Alibaba, both of which were pushing for greater adoption of their mobile payment networks—WeChat Pay and Alipay—through ride-hailing services.

In 2015, Didi and Kuaidi merged. Alibaba became an investor in the combined company, Didi Chuxing, but its stake is much smaller than Tencent’s and wasn’t listed in Didi’s listing prospectus. Both Tencent and Alibaba also have various business dealings with Didi.

—Raffaele Huang contributed to this article.

Write to Jing Yang at Jing.Yang@wsj.com