Representatives for Jagger in the United States did not return requests for comment.
The legendary singer and songwriter, who is 75 years old, announced over the weekend that he would need to postpone the band's upcoming US tour.
Rolling Stone reported that it had confirmed the details published by a website called Drudge.
"I'm so sorry to all our fans in America and Canada with tickets".
The news comes days after the band postponed its North American tour following doctors' telling Jagger he needed to take a break from touring to receive medical treatment.
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The US website Drudge Report, citing unidentified sources, said Jagger, 75, would undergo surgery this week in NY to replace a heart valve.
"I'm devastated for having to postpone the tour but I will be working very hard to be back on stage as soon as I can". The four valves include the mitral valve, tricuspid valve, pulmonary valve and aortic valve. Mechanical valves can last decades but require patients to go on blood thinners, while tissue valves tend to last 12 to 15 years but can also be fixed through less-invasive procedures. "But if what we are reading now is true, that is quite reassuring, because heart valve surgery is now rather commonplace".
"About 50 percent of people who have the problem will die in a couple of years if they don't have the surgery", he added in a video posted on Twitter.
Bandmates Keith Richards and Ronnie Wood expressed their support on social media.
"A big disappointment for everyone but things need to be taken care of and we will see you soon", Keith tweeted.
"We are deeply committed to our community, fans, attendees and partners and look forward to welcoming Mick and The Rolling Stones to Burl's Creek as soon as he has recovered", said the emailed statement.