Web monitoring company Net Applications said Firefox, which was developed by the Mozilla Foundation, had 6.17% of the market in February, compared to the 5.59% it had in January.
Mozilla said Firefox has been downloaded 27 million times since it was launched at the end of last year.
Net Applications gave Internet Explorer 89.04% of the market, compared to 90.31% last December. Internet Explorer's fall below 90% was predicted earlier this year by web monitoring company Websidestory.com.
As the market share of all other major browsers has been stable over the past months, Firefox's increasing usage is at the expense of Internet Explorer, said Net Applications.
The Mozilla Foundation was a result of the spin-off of open source technology by Netscape, whose main browser once had 80% of the market before it was usurped by Microsoft.
Microsoft is addressing the concerns of critics of Internet Explorer, who have claimed it could be made more secure, by releasing a beta of IE7 this summer.
This version, designed for users of Windows XP Service Pack 2, will offer better protection against phishing, spyware and other malware.
Firefox has fallen victim to at least two security vulnerabilities this year.