"There has to be a massive campaign. We have to think about all demographic groups," Cook said in a rare interview.
Speaking to The Daily Telegraph, Cook also said that "we tech companies must all create tools that help reduce the volume of fake news."
Other CEOs of leading technology companies, such as Facebook boss Mark Zuckerberg, have spoken about the problem in recent months. But Cook's comments were much more blunt.
According to the Telegraph, he said that invented stories and hoaxes "kill people's minds".
Apple CEO Tim Cook wants the tech industry to take action against the "fake news" that is polluting the web.
And he called the "false news" plague "a big problem in many people".
The term "fake news" was originally coined to describe online stories designed to deceive readers. Often these stories are shared on Facebook and other social networking sites to generate profits for the creators. Other times, the stories are essentially propaganda made for political ends.
These kinds of stories received wide attention before and after the American elections. Fictional stories with headlines like "Pope Francis Shocks the World, Approves Donald Trump for President" have won millions of clicks.
It can be very difficult for Internet users to differentiate between legitimate sources of information and counterfeits.
This is where companies like Apple come in.
In an interview with the Telegraph - part of a multi-day European trip - Cook said that "too many of us are just in the complaints category right now and have not figured out what to do. "
He advocated both technological and intellectual solutions.
"We need the modern version of a public service announcement campaign. It can be done quickly if there is a will," Cook told the newspaper.
What he described was music to the ears of media literacy advocates.
"It's almost as if a new course is necessary for the modern child, for the digital child," said Cook.
Some schools make scattered efforts to teach media literacy, with an emphasis on digital skills, but this is by no means universal.
When asked if Apple would commit to funding a PSA campaign, an Apple spokesperson said the company had no further comments on Cook's interview.
The Apple CEO also suggested that tech companies can help eliminate false stories, but added: "We must try to compress them without compromising freedom of speech and the press."
Apple's own Apple News app has been recognized as a relatively reliable place to find information.
The company "examines publishers who join Apple News," BuzzFeed noted in December.
And the app has a "concern reporting feature where users can report fake news or hate speech."
Facebook recently started working with fact-checkers to test "warning labels" that appear when users share fabricated stories.
Cook, in the newspaper interview, expressed optimism that the plague of "fake news" is "a short-term thing - I don't think people want it in the end".
CNNMoney (New York) First published February 11, 2017: 8:00 p.m. ET