The 16-year-old boy died at the scene, while a 13-year-old girl was in hospital with severe burns.
"A witness heard shouting, ran to the scene were the two youths were on fire, and called for help," said senior public prosecutor Werner Wolff.
There was no indication that anyone else was involved in the fire, he added. The apparent suicide bid happened Tuesday in a field in the small village of Eslohe, near Dortmund, in western Germany.
It was not immediately known why the youths would have wanted to kill themselves, Wolff said.
The Westdeutsche Allgemeine Zeitung reported that no suicide note had been found and authorities were examining computers and cell phones belonging to the two students.
Investigators were hoping to eventually speak to the girl, but she was so badly hurt that she couldn't speak, the newspaper reported.
Mayor Stephan Kersting said he hoped the small size of the community would help residents to cope with the incident.
"You know the families, you know the children. We express our condolences to the families," he said. "The whole community is in shock."