McChrystal, a former special operations chief, usually speaks cautiously in publicand has enjoyed mostly sympathetic US media coverage since he took over the Nato-led force last year.
"Throughout my career, I have lived by the principles of personal honour and professional integrity. What is reflected in this article falls far short of that standard," he said.
In the profile, McChrystal jokes sarcastically about preparing to answer a question referring to Joe Biden, the US vice-president, known to be a sceptic of the commander's war strategy.
He also told the magazine that he felt "betrayed" by Karl Eikenberry, the US ambassador to Kabul, in a White House debate over war strategy last year.
Referring to a leaked internal memo from Eikenberry that questioned McChrystal's request for more troops, the commander said that the ambassador had tried to protect himself for "for the history books".
"I like Karl, I've known him for years, but they'd never said anything like that to us before," McChrystal said in the article.
Eikenberry, himself a former commander in Afghanistan, had written to the White House saying Hamid Karzai, the Afghan president, was an unreliable partner and that a surge of troops could draw the US into an open-ended quagmire.
The article revisits the friction between the White House and the military last year as Obama debated whether to grant McChrystal's request for tens of thousands of reinforcements.
Al Jazeera's James Bays, reporting from Kabul, said that McChrystal managed to offend every single one of his key bosses with the statements in the article.
Our correspondent said that the Rolling Stone reporter managed to get high level access: "I met the reporter in Washington, DC, over a month ago after he came out of a meeting inside the White House with McChrystal's advisors.
"This incident shows the tensions that exist between the top advisors here in Afghanistan. What will happen now is how this agreement is viewed on Capitol Hill and on the Afghan street.
"The Taliban is also trying to win over the Afghan people. There is certainly very little disunity normally in the Taliban."
Meanwhile, as foreign forces in Afghanistan marked another grim milestone in their war against the Taliban, signs of cracks in the alliance surfaced.
After 10 soldiers were killed in a single day, there was further turmoil for Nato as Britain announced that Sherard Cowper-Coles, its special envoy to Afghanistan, was taking "extended leave".
William Hague, Britain's foreign secretary, is to review the post of special envoy to Afghanistan, the BBC reported.
The news of Cowper-Coles's departure came amid reports that he had clashed with military officials over strategy, just a month ahead of a crucial international conference in the Afghan city of Kabul.
The Guardian newspaper reported there had been serious disagreements in recent months between Cowper-Coles and officials from Nato.
It said that Cowper-Coles was convinced the military-focused counter-insurgency effort was headed for failure and wanted talks with Taliban fighters to be a priority.
The Taliban, however, has so far rejected a plan drawn up at a landmark Kabul peace meeting to give jobs and money to those who lay down arms.
Last month they promised a new campaign of attacks on diplomats, lawmakers and foreign forces.