The incident happened on Saturday afternoon as the Airbus A320 approached Hamburg airport on a flight from Munich.
Airline spokesman Wolfgang Weber said the plane was traveling at 155 mph when it was rocked by wind during its landing attempt.
The left wing grazed the runway for a moment, but Weber said the pilot was able to stabilize the aircraft and take off again in what he called an "absolutely professional maneuver."
The plane landed safely shortly afterward on its second attempt.
"It was a dicey situation," Weber said. "People were quite shaken."
"It is hard to describe it went very quickly," passenger Hansi Kuepper said on N-TV television. He said there was silence on board for several minutes after the incident.
The plane went back into service Sunday after repairs, Weber said.
Germany's Federal Bureau of Aircraft Accidents Investigation said it was looking into the incident. An expert with the office, Lothar Mueller, said it was examining why the runway in question was being used amid the gusting wind.
Axel Raab, a spokesman for Deutsche Flugsicherung, which runs German air traffic control operations, said he believed neither tower nor pilot had done anything wrong. He praised the pilot for "a very professional maneuver."
"I don't want to anticipate the results of the investigation, but at first sight no one has anything to answer for," he said, describing it as an "unfortunate circumstance" that the plane was caught by such a heavy gust of wind.