Apple’s move will force Facebook to redesign its messaging apps, two people familiar with the issue said. It may have a particularly heavy impact on WhatsApp, which has been using the internet calling feature in a variety of ways, including for implementing the app’s end-to-end encryption, the people said. Other messaging app developers, who have long relied on the internet calling feature to keep their apps running in the background on Apple mobile devices, will also have to rebuild their apps, said people familiar with the issue.

In a statement, a Facebook spokesperson said the company was not collecting data through the calling feature. “The changes to the upcoming iOS releases are not insignificant, but we are in conversations with Apple on how best to address,” the spokesperson said. “To be clear—we are using the PushKit VoIP API to deliver a world-class, private messaging experience, not for the purpose of collecting data.”

A spokeswoman for Apple did not have a comment.

The change comes as Apple and Facebook are embroiled in a fight over messaging—which is strategic to each for different reasons. Facebook is taking steps to unify its messaging services, which it sees as a way to keep its users loyal and engaged, and which could lead to new revenue streams around commerce and other services. But a stronger Facebook messaging service could threaten Apple’s iMessage, one reason why people keep buying iPhones.

Apple is making the change in the September rollout of its new mobile operating system, iOS 13. App developers have until April 2020 to comply with the new specifications. While the change was announced in a breakout session at its annual Worldwide Developers Conference in June, it has received very little public attention since then.

Debate about how app makers use the internet calling feature, which relies on a technology called Voice over Internet Protocol, or VoIP, has been simmering for years. After Facebook split off messaging into a standalone Messenger app in 2014, the social media giant tried to keep the technology in its main app. But Apple figured out what Facebook was doing and made it stop, said Phillip Shoemaker, who until 2016 was the head of Apple’s app review team. But Messenger and WhatsApp, which allow internet voice calls, still use the feature.

“Messenger can still use [VoIP background] mode, and does,” said Mr. Shoemaker. “What they do in the background, whether it be accept calls, listen in all the time or update the content of the main app, it’s all unclear to Apple, but could be happening.”

Aside from potentially gathering data, the feature also sucks up system resources, shortening battery life. The impact on battery life briefly made it into the headlines back in 2015 when it was discovered that the main Facebook app was using the voice-calling feature to run in the background.

Other major messaging apps like Snapchat and China’s WeChat have been using the feature to run in the background for a number of reasons unrelated to voice calling, one of the people familiar with the issue said. Snap had no immediate comment, and WeChat didn’t respond to a request for comment.

Privacy Battles

Apple cited the need to protect privacy and to improve performance of its devices when it unveiled the change to the internet calling feature at the Worldwide Developers Conference. Apple CEO Tim Cook has come out forcefully on the need to protect privacy in recent years. “Our own information, from the everyday to the deeply personal, is being weaponized against us with military efficiency,” he said at a privacy conference in Brussels last year.

Although Apple has been rolling out a number of features to protect user privacy in the software running on its devices, iOS 13 is especially robust when it comes to privacy. One new feature, for example, gives users more options to limit location tracking by apps. The biggest headline grabber coming out of its June developer conference was “Sign in with Apple,” a privacy-centric single sign-on feature that competes with Google and Facebook.

As Apple has ramped up its privacy push, it has targeted Facebook. Earlier this year, for example, Apple shut down Facebook’s ability to distribute iOS apps to its own staff for testing following a TechCrunch report that Facebook was violating Apple’s rules by distributing a data-gathering app outside of the App Store to non-employees as part of a paid survey program.

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Facebook is well aware of the kind of impact these changes could have on its bottom line. Upcoming features in Google’s Android operating system also include many limits on apps running in the background. In response to a question during a recent earnings conference call about near-term challenges for the company, Facebook CFO David Wehner said they include “platform changes as it relates to operating systems and more of a focus on privacy from the operating systems, and the impact that that can have on measurements and also on targeting.”

—Alex Heath contributed to this article