The claims of unwanted kissing and touching have been published in the New Yorker magazine.
In a statement, CBS said it was looking into the allegations and would “take appropriate action”.
Mr Moonves, 68, told the magazine that he “may have made some women uncomfortable” in the past.
“Those were mistakes, and I regret them immensely,” he said. “But I always understood and respected… that ‘no’ means ‘no,’ and I have never misused my position to harm or hinder anyone’s career.”
CBS’ stock price dropped by 6% on Friday as reports of the New Yorker article trickled out.
The exposé is by Ronan Farrow, who this year won a Pulitzer Prize for detailing assault accusations against Hollywood producer Harvey Weinstein.
Some of the alleged incidents are said to have occurred more than 20 years ago.
In a statement, CBS said: “All allegations of personal misconduct are to be taken seriously.
“The Independent Directors of CBS have committed to investigating claims that violate the Company’s clear policies in that regard.
“Upon the conclusion of that investigation, which involves recently reported allegations that go back several decades, the Board will promptly review the findings and take appropriate action.”
Mr Moonves, who is chairman and chief executive of CBS, has yet to respond to BBC requests for comment.
Six women have made allegations against him, including the actress Illeana Douglas who told the New Yorker that he violently kissed her.
“The physicality of it was horrendous,” she said. “You think, how long is this going to go on? I couldn’t get him off me.”
All of the women say they believe their careers suffered because they rejected his advances.
A CBS statement on behalf of Mr Moonves said he acknowledged trying to kiss Ms Douglas but denied sexual assault and intimidation.
Earlier this year, CBS’ fired veteran presenter Charlie Rose, who was accused of sexual harassment by a number of women, including several CBS employees.
Mr Moonves has long been considered one of the most powerful men in Hollywood, helping steer the network broadcaster into the digital age.
Analysis by James Cook, BBC Los Angeles
He started out as a TV actor before developing Friends and ER with Warner Bros and then reviving an ailing CBS with hits including CSI, Everybody Loves Raymond and, most recently, The Big Bang Theory.
For a decade under his leadership, CBS has been the most-watched network in the US, narrowly retaining its crown ahead of NBC in the 2017-18 season.
Mr Moonves earned $69.3m (£53m) in 2017 making him one of the highest paid chief executives in the world.
But his tenure at the top of the network, which he joined in 1995, has been marked by a power struggle with Shari Redstone who, through her family’s business National Amusements, is the controlling shareholder in both CBS and the media conglomerate, Viacom.
Ms Redstone and Mr Moonves are currently battling in the courts as he tries to thwart her plan to merge the two companies.
He has been married to Julie Chen – host of CBS’ Big Brother – since 2004.
The two wed less than two weeks after he finalised his divorce from Nancy Wiesenfeld, to whom he had been married since 1978, according to the Hollywood Reporter.
During the 2016 presidential election, he was criticised for saying Donald Trump’s candidacy “may not be good for America, but it’s damn good for CBS”.
“The money’s rolling in and this is fun,” he said at a media event in San Francisco.