Probably the best-known example would be Chaucer; humor in The Canterbury Tales runs the gamut, from poop jokes to irony and satire. "The Miller's Tale" is a good starting point, featuring slapstick, puns, and body humor. Others, like "The Summoner's Tale," satirize corruption among the clergy. There are many translations from the Middle English, but I don't know which one is currently the preferred rendering among Chaucer scholars. In any case, a translation is likely to be missing some of the word play, but--not unlike Shakespeare--unless you're familiar with the spoken language of the period as well as the lexicon, it's easily missed by modern readers.

As a side note, "The Miller's Tale" belongs to a comic genre known as the fabliau. Indeed, Chaucer drew upon French examples in writing The Canterbury Tales. You can find out more here.

The riddles of the 10th-century Exeter Book can be poetic, witty, or bawdy--positively ribald, even. See riddle 25.

My personal favorite would be the Viking graffiti found inside Maeshowe, a tomb in Orkney dating to the 3rd millennium BCE. I refer, of course, to the elegant, the profound, the poignant inscription: "Þorný fucked, Helgi carved."