Team boss Niki Lauda lamented Hamilton's run of 'unfair' bad luck which greatly hinders his chances in Sunday's race.
The fire, at the rear of his car, ruled him out of contention for pole position without clocking a time. It was his fourth car problem of the season compared to just one to have affected his team-mate and title rival.
"It looks like a fuel leak, but we have go to get it back and see. The fuel pressure went down and there was a fire, so... " said Lauda. "It is completely unfair on Lewis and especially as he was fastest all weekend and would have won the race.
Hamilton said: "I don't know what I can do tomorrow -- it's a track you can't really overtake on. Its's going to be a struggle to make the top ten or at least top five.
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"I'll leave here more than 20 points behind Nico, but there's still races to go. I will try my best."
He added: "I had bailed out on that lap and wanted to try on my second, for a time. Something happened - something failed in the brakes and then the engine died.
He parked the car at the pit lane entry in front of a group of marshals who put the fire out as Hamilton walked dejectedly with his head down towards the team garage.
The fire came seven days after Hamilton was the victim of a high-speed brakes failure at the German Grand Prix and wrecked his hope of claiming a first pole position in seven races at one of his most favourite circuits.
Hamilton is 14 points behind Mercedes team-mate Nico Rosberg in the title race and Saturday's setback handed his rival a potential gift of pole position for the third time in four races.
The 29-year-old Briton made an error of judgement and pitted in the final minutes of qualitying at the British Grand Prix and had a high-speed crash at Hockenheim last weekend.
Hamilton was not the first driver to be eliminated on Saturday. Venezuelan Pastor Maldonado of Lotus had already pulled up without a clocked time in the first minute.
Hamilton was unhurt. The team issued a brief comment on Twitter: "We are analyzing the data to understand what happened with @LewisHamilton's car and why.