"anything that befalls of ruinous or distressing nature; any unfortunate event," especially a sudden or great misfortune, 1590s, from Middle French désastre (1560s), from Italian disastro, literally "ill-starred," from dis-, here merely pejorative, equivalent to English mis- "ill" (see dis-) + astro "star, planet," from Latin astrum, from Greek astron "star" (from PIE root *ster- (2) "star").
The sense is astrological, of a calamity blamed on an unfavorable position of a planet, and "star" here is probably meant in the astrological sense of "destiny, fortune, fate." Compare Medieval Latin astrum sinistrum "misfortune," literally "unlucky star," and English ill-starred.