This seemed like a spoof or a joke to me so I looked into it and the best information I found was on Wikipedia:
Hippopotomonstrosesquipedaliophobia — fear of long words. Hippopoto- "big" due to its allusion to the Greek-derived word hippopotamus (though this is derived as hippo- "horse" compounded with potam-os "river", so originally meaning "river horse"; according to the Oxford English, "hippopotamine" has been construed as large since 1847, so this coinage is reasonable); -monstr- is from Latin words meaning "monstrous", -o- is a noun-compounding vowel; -sesquipedali- comes from "sesquipedalian" meaning a long word (literally "a foot and a half long" in Latin), -o- is a noun-compounding vowel, and -phobia means "fear". Note: This was mentioned on the first episode of Brainiac Series Five as one of Tickle's Teasers.
Elsewhere, however, the consensus seems to be that the relatively brief 'sesquipedaliophobia' would be sufficient to convey the meaning.
Yet another suggestion I came across for a word meaning 'fear of long words', and my personal favourite, is 'megalogophobia'. Not to be confused with a fear of a certain Philippine language, which of course would be Tagalogophobia...
(We've actually written about phobias on this blog before, most notably hobophobia and pogonophobia.)