1840, from pyro- "fire" + mania "madness, frenzy." Used in German in the 1830s.
The propensity which leads an insane person to accomplish his purpose by burning, has been considered to merit particular notice, and to constitute a variety of monomania. Dr. Marc, of France, has published a memoir on the subject; he gives the name of pyromania to it, and considers that, like other insane propensities, it may be the result of instinct, or it may be the result of delusion--reasoning upon erroneous principles. [Alexander Morrison, M.D., "The Physiognomy of Mental Diseases," London, 1840]
An older word for it was incendiarism.