From Middle High Germanwefse, webse, wespe, from Old High Germanwefsa. The forms with -sp- come from Middle Low Germanwespe, from Old Saxonwespa (10th century, alongside older wepsia), spreading to Middle High German in the 12th century. Some Upper German dialects retain the original consonantism to this day, e.g. Swabish Wefz, Bavarian Weps, Webes. The spread of -sp- was reinforced, if not triggered, by Latinvespa. Popular association with the verb wispeln from Old High German hwispalōn(“to whir, to whisper”) is also likely; compare Central FranconianWespel(“wasp”).
Cognates include Dutchwesp, Englishwasp, Frenchguêpe. These are often traced back to Proto-Germanic*wapsō- or *wepsō-, from Proto-Indo-European*wobʰseh₂(“wasp”), pertaining to *webʰ-(“to weave”). There are some formal problems to this particular reconstruction, however, most importantly the fact that Germanic *wapsō- is an anomalous form lacking the expected effect of Primärberührung.