The world championship leader, challenging for his third pole position of the year (having started at the front at Silverstone and Hockenheim), was fastest of all in the first two segments of qualifying.
But he drifted way off the pace in Q3 before settling for 10th and heading back into the pits, while his team-mate Felipe Massa qualified third.
"It's a shame because I think it would have been the easiest pole position of the year for us," said Alonso.
"We did 1m24.1s in Q1 with an easy lap and then looking at it, 1m24.0s was, let's say, easy for us to do.
"We lost one big opportunity but nothing we can do now. We'll try to be strong tomorrow, the car will be fixed and we will see what we can do from 10th.
"Something broke in the car in Q3, so we had no time to fix it, so we went out just to see if we could beat some of the cars but unfortunately we were not able because we lost too much performance," he added.
Ferrari team principal Stefano Domenicali confirmed that it was an issue with the rollbar.
"It seems to be [a problem] with the rear bar," the Italian told Sky. "It seems to be a mechanical failure. We need to wait for the car to come back.
"We knew that the car was not good because Fernando understood exactly the situation straight away, so that's very unfortunate but that's the way it is.
"Of course we are very disappointed because we could have done a great qualifying with Fernando and at least we are pleased that Felipe did a good job. He is there just behind the McLarens."