When Apple launches its new software update for the iPhone on Wednesday, users will be offered the chance to surf the mobile Web without annoying ads cluttering up their screen.

But Apple’s support for ad-blocking technology is ringing alarm bells on Madison Avenue, where critics warn it threatens not only the lifeblood of their business — but also the economic underpinnings of the free Internet.

“We don’t think ad blocking is right,” Scott Cunningham, senior vice president of the Interactive Advertising Bureau, told The Post.

The rise of ad blockers is one of the biggest sea changes to affect the Internet ad business in decades, Cunningham said. For years, publishers have made what they believe is a fair trade-off with readers.

“Advertising is the economic engine that drives the free Internet,” Cunningham said. “The reality is the last 20 years have seen people developing content online for distribution, and consumers have opted in for that free content.”

While use of ad-blocking technology on desktop computers and mobile devices has been on the rise, Apple’s commitment to it is a game changer. With iOS 9, developers will be able to create ad-blocking software for Apple’s Safari mobile browser.

Apple’s goal appears to be making the mobile Web a faster, cleaner and more pleasant all-around experience. But it could also have the effect of pushing publishers off the mobile Web and toward subscription services and paid apps, which is an area dominated by Apple.

Already some Web publishers and content providers are turning away consumers who avail themselves of ad-busting technologies. Hulu is rejecting customers who use ad blockers, while the Washington Post blocks consumers from reading its site if it detects an ad blocker — and redirects them to subscription pages, according to trade magazine Advertising Age, which ran an alarmist story on Monday entitled, “Yes There’s a War on Advertising. Now What?”

Whatever Apple’s new ad-free vision is, executives across Madison Avenue are scrambling to figure out the ramifications.

“The free Internet is going to have a major problem, and that’s a concern for all of us,” Steve Carbone, the head of digital at MediaCom, told The Post, “It’s a huge issue.”

MediaCom is part of media-buying giant GroupM, which is preparing to update clients on what it means for them.

PageFair, a company that detects ad blockers, estimates there are 198 million users of ad blockers worldwide, including 45 million in the US — and it’s growing. The technology is particularly concentrated for users of gaming and tech sites and among millennials who advertisers most want to reach.

Global mobile-advertising spending is predicted to hit $100 billion in 2016, according to eMarketer.

Some Web publishers are working on technology that skirts ad blockers and serves up advertising regardless. That has some on Madison Avenue worried that consumers will blame their clients for overriding technology rather than the publishers.

“I can’t stop the progression of technology,” MediaCom’s Carbone said. “I can only adapt to it.”