Related phrases: much ado about nothing, making a song and dance about nothing
Origin: The phrase was first used by Lucian (120-200 AD), the Greek satirist, in Ode to a Fly, although the comparison was initially between an elephant and a fly: “elephantem ex musca facere.” The idiom was included in Eramus’s collection of Greek and Latin proverbs, Adagia, published and revised from 1500-1536. In 1548, Nicholas Udall, an English cleric and playwright who was tutored by Thomas Cromwell, translated Eramus’s book as The First Tome or Volume of the Paraphrase of Erasmus upon the Newe Testamente. In Udall’s scholarly work, the phrase appears as: “The Sophistes of Grece coulde through their copiousness make an Elephant of a flye, and a mountaine of a molehill.” Lexicographer William Safire notes that it was Udall who actually added the “mountain” and the “molehill” to the original Latin expression. Why Udall felt compelled to add the mountain and molehill is anybody’s guess (perhaps he favored alliteration, analogous metaphors, or perhaps he was simply battling a severe mole infestation in his garden). Safire also points out an error in the OED, that mistakenly credits the first recorded use of mountain and molehill to John Foxe, a British historian, in 1570 — 22 years later than Udall. Author Max Cryer suggests that it was Thomas Bacon who used the phrase in Catechism (1563) that helped popularize the phrase.
For further reading: Common Phrases and the Amazing Stories Behind Them by Max Cryer, Skyhorse Publishing (2010)