late 15c., from Old English fneosan "to snort, sneeze," from Proto-Germanic *fneusanan (compare: Middle Dutch fniesen, Dutch fniezen "to sneeze;" Old Norse fnysa "to snort;" Old Norse hnjosa, Swedish nysa "to sneeze;" Old High German niosan, German niesen "to sneeze"), from Proto-Germanic base *fneu-s- "sneeze," of imitative origin, as is PIE *pneu- "to breathe" (source of Greek pnein "to breathe").
Other imitative words for it, perhaps in various ways related to each other, include Latin sternuere (source of Italian starnutare, French éternuer, Spanish estornudar), Breton strevia, Sanskrit ksu-, Lithuanian čiaudėti, Polish kichać, Russian čichat'.
English forms in sn- might be due to a misreading of the uncommon fn- (represented in only eight words in Clark Hall, mostly in words to do with breathing), or from Norse influence. OED suggests Middle English fnese had been reduced to simple nese by early 15c., and sneeze is a "strengthened form" of this, "assisted by its phonetic appropriateness." Related: Sneezed; sneezing. To sneeze at "to regard as of little value" (usually with negative) is attested from 1806.