Alexander, who retired on March 31, made the comments in an interview with The Australian Financial Review newspaper to be published on Thursday, a transcript of which was made available to Reuters ahead of publication.
Alexander, the longest-serving Director of the NSA, also spoke in favour of backing Japanese militarization to counter-balance China and warned that a lack of norms governing cyber-conflict could trigger a war between traditional foes like North and South Korea.
Civil libertarians in the United States and Washington's allies in Europe were shocked by the extent of U.S. surveillance revealed by Snowden, and a handful of U.S. congressmen have alleged that he was acting at the behest of a foreign government.
Snowden, who fled to Moscow last year, has dismissed the allegations. He expects his temporary asylum status in Russia to be renewed before it expires in summer, according to his lawyer.
"I think he is now being manipulated by Russian intelligence. I just don't know when that exactly started or how deep it runs," Alexander said.
"Understand as well that they're only going to let him do those things that benefit Russia, or stand to help improve Snowden's credibility. They're not going to do things that would hurt themselves. And they're not going to allow him to do it."
In the interview, Alexander described a traditional global security order that has been disrupted by rapid developments in offensive cyber technology, with the potential for unintended consequences rising as a result.
A 2012 cyber-attack on government oil company Saudi Aramco believed to have originated from Iran, he said, had been routed through servers in the United States and inadvertently almost disabled a major telecommunications company there.
An attack on South Korea's banking system in 2013 that was believed to have originated in the North, he said, was an example where unintended consequences could accidentally have triggered a shooting war.
"I'm concerned there is a rising chance that individuals and/or nation states miscalculate because they don't know where the red lines are. And this problem of a lack of transparency on red lines, and agreed escalation protocols, is especially acute in cyber-space," he said.
Alexander, who was succeeded by U.S. Navy Vice Admiral Michael Rogers, also signalled his concern over Chinese claims on the oil and gas-rich South China Sea that have increased tension in Asia, arguing that the U.S. should back Japan as a counterbalance Beijing's rise.
"If China continues to act aggressively, I believe we should welcome Japan's increased militarization," he said.
He praised Australia's decision last year to ban China's Huawei Technologies Co Ltd from bidding for work on the country's $38 billion National Broadband Network (NBN) over cyber-security concerns.
The U.S. House Intelligence Committee last year described Huawei as a national security threat and urged American firms to stop doing business with the Shenzhen-based company. Huawei has denied the U.S. allegations that its equipment could be used by Beijing for espionage.
"I think what Australia did on the Huawei decision was tremendous," he said.