The attackers target only Windows users so far, but Adobe advises all users to update their software.
According to Adobe and to Symantec researchers, the attacks take form of a variety of spam emails containing specially crafted malicious attachments.
"For the exploit to successfully work, the malicious attachments need to be opened on a computer with a vulnerable version of Adobe Flash Player," Symantec researchers reveal.
"The malicious documents contain an embedded reference to a malicious Flash file hosted on a remote server. When the Flash file is acquired and opened, it sprays the heap with shellcode and triggers the CVE-2012-0779 exploit. Once the shellcode gains control, it looks for the payload in the original document, decrypts it, drops it to disk, and executes it."
Vulnerabilities in Adobe's products in general and Flash Player in particular are often exploited by cyber attackers, so the company introduced silent automatic updating for Flash Player on Windows in March, and is working on releasing a stable Flash Player for Mac with the feature soon.