Media investors breathed a sigh of relief last week after Walt Disney CEO Bob Iger assuaged industry concerns about the rate of consumers dropping premium subscription channel cable packages — otherwise known as cord cutting — on the company earnings call.

However, according to one widely followed analyst, those concerns should not be put on the back burner as media stocks are in for a rude awakening.

"There is a seismic change in consumer behavior that is affecting the entire media sector," said BTIG's Rich Greenfield on "Fast Money" last week.

"It's not just a Disney issue, a Time Warner issue, a Discovery issue," he said. "Every one of these companies is facing the issue that consumers are simply less and less interested in watching live linear television," said Greenfield.

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Recently, Magid Advisors surveyed 2,400 consumers and found that among key demographics, cord cutting was intensifying at breakneck speed. According to Magid, 3.7 percent of pay TV subscribers age 18 to 64 said they were "extremely likely" to cancel their pay TV service in the next 12 months, up nearly 3 percent from last year and a jaw-dropping 95 percent increase over results from 2011.

The phenomenon benefits streaming media companies like Hulu and Netflix, where consumers pay to stream shows, movies and original content of their choosing and on demand, without having to pay for channels they may not watch. The changing landscape has prompted companies like HBO and CBS to develop their own streaming options recently.

While investors rewarded Disney's results by bidding up the stock, they punished shares of Time Warner over concerns about cable subscription fees. According to Greenfield, when consumers are faced with the choice of choosing and expensive bundle over-the-top alternative, they will look to the cheaper alternatives.

"Consumers are not dumb. They're making decisions and more of them are cutting or shaving the cord, and it's affecting every one of these companies in the sector," he said.

Many of the cable companies have explored streaming options to combat fleeting young viewership — but Greenfield says the problem exists in content.

"The whole industry needs to reorient itself — invest heavily in great, must-watch programming, and build the technology to go direct to consumer and support customer care," said Greenfield.