However, CNBC's Jim Cramer said he wouldn't recommend selling cable stocks, even on this news.
"They've been so good," he said on "Squawk on the Street." "They've been unbelievable."
Time Warner Cable was down 7 percent, Comcast, CNBC's parent company, dropped nearly 6 percent and Verizon fell almost 2 percent following the announcement. They have since regained some of those losses.
In his statement, the president called on the FCC to create a new set of rules "protecting neutrality and ensuring that neither the cable company nor the phone company will be able to act as a gatekeeper, restricting what you can do or see online."
Read MoreWhat is net neutrality?
Amy Yong, vice president at Macquarie Research, told "Street Signs" that while investors were surprised by Obama's announcement Monday, it will be a while before the FCC acts.
"It would take one to two years at best if there was going to be a reclassification of broadband," she said. However, "there is a lot of M&A activity in this space right now … so there's a lot at stake here."
And it's not only large, public companies that will be affected by stricter rules, Yong pointed out.
"There's still a lot of companies, like Mediacom, Cox, that are all in the hands of private families," she said. "If there is regulation, that would hurt a lot of those smaller businesses."
She predicts the FCC will stick with its proposed "hybrid" version of broadband regulation that would leave residential service alone, but would have some sort of regulation on the commercial side.
Yong continues to likes Charter Communications, giving it an "outperform" rating and $225 price target.
—CNBC's Drew Sandholm, CNBC's Jackie O'Sullivan and Reuters contributed to this report.
Disclosure: Macquarie Capital (USA) INC or one of its affiliates is currently managing or co-managing a public offering of securities of Charter Communications Inc.