Cern spokesman James Gillies said on Saturday that the sector that was damaged would have to be warmed up from its operating temperature - of near absolute zero - so that repairs could be made, and then cooled down again.
While he said there was never any danger to the public, Mr Gillies admitted that the breakdown would be costly.
He said: "A full investigation is still under way but the most likely cause seems to be a faulty electrical connection between two of the magnets which probably melted, leading to a mechanical failure.
"We're investigating and we can't really say more than that now.
"But we do know that we will have to warm the machine up, make the repair, cool it down, and that's what brings you to two months of downtime for the LHC."
David Shukman heads deep underground to take a look at the LHC's tunnel
The first beams were fired successfully around the accelerator's 27km (16.7 miles) underground ring over a week ago.
The crucial next step is to collide those beams head on. However, the fault appears to have ruled out any chance of these experiments taking place for the next two months at least.
The quench occurred during final testing of the last of the LHC's electrical circuits to be commissioned.
At 1127 (0927 GMT) on Friday, the LHC's online logbook recorded a quench in sector 3-4 of the accelerator, which lies between the Alice and CMS detectors.
The entry stated that helium had been lost to the tunnel and that vacuum conditions had also been lost.
The superconducting magnets in the LHC must be supercooled to 1.9 kelvin (-271C; -456F), to allow them to steer particle beams around the circuit.
As a result of the quench, the temperature of some magnets in the machine's final sector rose dramatically.
The setback came just a day after the LHC's beam was restored after engineers replaced a faulty transformer that had hindered progress for much of the past week.
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