"Again we see these leaks to the media about ongoing operations, which is incredibly disturbing. Doesn't this give some benefit to our adversaries?" McCain told reporters in Singapore, where he was attending a summit on Asian security.
McCain, who was defeated by Obama in the 2008 presidential election, said there had been ill-advised leaks previously that revealed details of the US raid last year that killed Al-Qaeda leader Osama bin Laden and other operations.
"We know the leaks have to come from the administration. And so we're at the point where perhaps we need an investigation," said McCain, the most senior Republican on the Senate Armed Services Committee.
"So this is kind of a pattern in order to hype the national security credentials of the president and every administration does it. But I think this administration has taken it to a new level."
The New York Times reported Friday that Obama accelerated cyberattacks on Iran's nuclear program using the Stuxnet virus, and expanded the assault even after the virus accidentally made its way onto the Internet in 2010.
The operation, begun under president George W. Bush and codenamed "Olympic Games," is the first known sustained US cyberattack ever launched on another country, employing malicious code developed with Israel, according to the Times.
McCain said he believed the US president had authority to launch such an attack.
"But I also believe that it would be helpful if he talked to a select few leaders of Congress. Most presidents have done this," he said.
The White House "never" briefed lawmakers on the assault, he said.
The Times said its report was based on 18 months of interviews with current and former US, European and Israeli officials, and was adapted from the book "Confront and Conceal: Obama's Secret Wars and Surprising Use of American Power," by David Sanger, set to be published next week.
The cyberattack, aimed at preventing Iran from developing nuclear weapons, sowed widespread confusion in Iran's Natanz nuclear plant, the newspaper said.