He noted hackers recently figured out a fairly sophisticated way to attack Macs by exploiting a flaw in Adobe's Flash software.
"The only thing that was making it safe before is that nobody bothered to attack it. That goes away if somebody bothers to attack it," Miller said.
Cyber security attacks have been on the rise. In last week's State of the Union address, US President Barack Obama issued an executive order seeking better protection of the country's critical infrastructure from cyber attacks.
Over the weekend, cyber security specialists Mandiant reported a secretive Chinese military unit was believed to have orchestrated a series of attacks on US companies, which Beijing has strongly denied.
White House spokesman Jay Carney said on Tuesday that the Obama administration has repeatedly taken up its concerns about Chinese cyber theft with Beijing, including the country's military. There was no indication as to whether the group described by Mandiant was involved in the attacks described by Apple and Facebook.
An Apple spokesman declined to specify how many companies had been breached in the campaign targeting Macs, saying he could not elaborate further on the statement it provided.
"Apple has identified malware which infected a limited number of Mac systems through a vulnerability in the Java plug-in for browsers. The malware was employed in an attack against Apple and other companies, and was spread through a website for software developers," the statement said.
"We identified a small number of systems within Apple that were infected and isolated them from our network. There is no evidence that any data left Apple," it continued.
The statement said Apple was working closely with law enforcement to find the culprits, but the spokesman would not elaborate. The FBI declined to comment.
Apple said it plans to release a piece of software on Tuesday, which it said customers can use to identify and repair Macs infected with the malware used in the attacks.
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