The tow vehicle was steering the plane towards a departure gate to pick up passengers bound for the United States when it went up in flames for reasons unknown, a spokesman for the German airline said.
The fire spread from the truck to the plane, with photographs showing a massive column of black smoke.
The plane was empty but "ten people are being treated with respiratory irritations".
The plane was so severely damaged by the flames that it has been grounded. The incident did not disrupt traffic at Frankfurt airport, Germany's busiest hub.
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