Team boss Ron Dennis said the 22-year-old rookie was unhurt but it is too early to say whether he would start on Sunday at the Nuerburgring.
"He has no pain, no broken bones and did not lose consciousness. We won't decide for a couple of hours," he told ITV television.
A team spokeswoman said that the Briton, who ploughed into the tyre wall five minutes before the end of qualifying, was conscious and talking.
Hamilton, wearing an oxygen mask and with a drip applied, waved and gave a thumbs-up sign as he was taken to a waiting ambulance.
The session was red flagged when his McLaren suffered what looked like a suspension failure, with the tyre bursting and leaving him as a mere passenger while the car sped across a gravel trap.
Dennis, who immediately left the pit lane wall, said a faulty air gun appeared to be to blame.
"Effectively the wheel wasn't properly put on," he told the television.
"But
"We could tell from that it was a gun failure. At least we know we don't have a problem with the car."
Hamilton remained in the car, jiggling his legs, before trying to extricate himself. He stood up but remained in the cockpit, leaning against the airbox.
After getting out of the car, the Briton then dropped to the ground with marshals around him.
Hamilton is 12 points clear of team mate and double world champion Alonso, with eight races remaining including Sunday's.
The youngster has finished his first nine races on the podium and had been hoping to become only the third driver, after Michael Schumacher and Alonso, to rack up 10 podium finishes in a row.
Hamilton had been fifth in qualifying when the accident happened. He ended up 10th.
Image: McLaren Mercedes driver Lewis Hamilton is stretchered away by paramedics from his damaged car during qualifying for the European Grand Prix at Nurburgring on Saturday.