Wordorigins.org

What monkey wrenches have to do with monkeys is unknown. The term monkey has been used for a variety of devices, from cannons to pile-drivers, and it seems likely that the wrench’s name is related to this usage, but exactly how is uncertain.

This term for a wrench with an adjustable jaw dates to the early 19th century and is originally British, although now it is chiefly North American in usage. From a citation believed to be from 1807 that appears in E.S. Dane’s Peter Stubs & Lancashire Hand Tool Industry:

Fleetwood, Richard...Parr, Rainford. Screw plates, lathes, clock engines...monkey wrenches, taps.

The phrase to throw a monkey wrench into the machinery dates to 1918. From the American Economics Review of that year:

Mr. A. Paladini, one of the larger wholesale dealers...threw a monkey wrench into the machinery of proposed fish distribution.

Although the metaphorical sense of throwing a monkey wrench, meaning an obstacle or hindrance, is a bit older. On 30 July 1907 the Chicago Tribune published the following:

It should look to them as if he were throwing a monkeywrench into the only market by visiting that Cincinnati circus upon the devoted heads of Kentucky’s best customers.

The British version of this phrase, to throw a spanner into the works, dates to 1934. From P.G. Wodehouse’s Right Ho, Jeeves of that year:

He should have had sense enough to see that he was throwing a spanner into the works.

It has been suggested that the monkey in monkey wrench is an alteration (folk etymology) of the inventor’s name, a certain Charles Moncky of Baltimore who allegedly invented it 1858. Unfortunately for this explanation, the term is British in origin and predates Moncky by some decades.

(Source: Oxford English Dictionary, 3rd Edition)