The firm normally issues patches at a set time each month but said that the attention the problem had received forced it to move more quickly.
It follows the French and German governments decision to advise citizens to use other browsers.
Security experts said they had seen malicious code exploiting the weakness.
If a web user were to visit a compromised site using a vulnerable browser, they could become infected with a "trojan horse", allowing a hacker to take control of the computer and potentially steal sensitive information.
Microsoft said on 18 January that there were "very few" infected sites on the web.
But Security firm Sophos said now it had seen "copycat" sites trying to exploit the vulnerability.
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