FORTUNE — It sounded pretty good until Eric Schmidt said it: Siri, the so-called personal assistant app on Apple’s iPhone 4S, is the new face of search. Siri is threatening to sideline the tried-and-true search box that Google turned into a cross between a wishing well and the most trusted way to navigate a rapidly sprawling web. Some said that Google should be concerned. Others, predictably, overreacted and labeled Siri a “Google killer.”

Then last week Google’s (GOOG) former CEO and current chair released his responses to Senate subcommittees looking into Google’s dominance in the search industry. In the past few years, Schmidt has transitioned from a seasoned and successful CEO to something of a loose cannon who spends most of his time retracting, or explaining or laughing away his previous statements. So when Schmidt, citing some of those commentators who saw Apple’s (AAPL) Siri as a Google competitor, suggested that Siri could be a force in search, he drew a skeptical response. Some said Schmidt was just downplaying Google’s prominence in search. Others pointed out that Siri’s own default search engine is Google.

But how can Google be a monopoly that is about to get its clock cleaned by Apple? The truth is less certain, if equally dramatic: The search industry is in the early stages of a disruptive period of change. It will look more like Siri than Google does today — that is, it will have a more intuitive AI feel to it. Apple and Google — and maybe even Microsoft (MSFT) — will play a key role in shaping it. Which means it’s well past time to be worrying about whether Google is a monopoly.

In fact, Google isn’t a even search monopoly anymore. It controls around two thirds of the search market. That statistic was more significant several years ago, before the rise of specialized searches through sites like Yelp for restaurants, Kayak for travel and Twitter for real-time chatter. Google is also said to have 97% of mobile search. But again, that overlooks the fact that most people access the mobile web through apps, not browsers.

In a way, search has always been about connecting us with the information we need on the web. Before search, there were directories like Yahoo (YHOO) and Excite. Then AltaVista and Inktomi built search engines based on the simple search box, and Google cleaned up, first by building a better search box and then by continually improving it. Google’s impact on search wasn’t a sudden revolution but a gradual progression that — only in retrospect — seems profound.

Now Apple has found a way to advance search in an equally dramatic way: Siri. There’s no search box to type into. You just ask. The idea of voice-activated search has been around for some time. Nuance Communications (NUAN), whose technology reportedly powers Siri, has long sold its Dragon voice-recognition software that can surf the web by voice. And Google’s mobile search app can type spoken queries into its search box.

But Siri is more than voice recognition. It’s a form of AI that takes a few more steps closer to an app that could pass the Turing test. People are still uncomfortable with any AI application that could be mistaken for a human, but the Easter-egg answers Apple has snuck into the app defuses any potential discomfort, and in fact gives Siri a conversational interface that feels far more personal that Google’s spartan home page.

It’s that conversational interface that poses the threat to Google. No longer is the search box the front-end of searches on the iPhone 4S. Google is the back-end technology that is suddenly less visible. Or rather, one of the back ends. Because of the rise of specialized searches like Yelp and Wolfram|Alpha, Siri can easily bypass Google’s search algorithms for many queries.

Google has another reason to be worried about Siri: It’s the closest thing we have to a mass-market phone app. For years, Google cast itself as a tech company at the forefront of artificial intelligence. Back in 2004, Google’s Sergey Brin talked about a future where AI would let you say into a phone “what you want to search for, and it will be pulled up.” Google reached that goal before Apple did, but now Apple has raised the bar much higher.

Google saw search as an entry point into artificial intelligence. Apple saw it the other way around — Siri’s AI was its way of helping people navigate the web. The question isn’t whether Siri is a search engine that can replace Google’s search box. It’s a different kind of search — that is, it’s the future of search.

Google will no doubt come back with its own AI innovations to search. That’s why Siri won’t be a Google killer. It will instead be a Google competitor in Google’s core market. Both companies will shape how we find information on our phones, which means the search industry is about to see some interesting changes in the coming years.