late 14c., "force-meat, stuffing;" 1520s, in the dramatic sense "ludicrous satire; low comedy," from Middle French farce "comic interlude in a mystery play" (16c.), literally "stuffing," from Old French farcir "to stuff," (13c.), from Latin farcire "to stuff, cram," which is of uncertain origin, perhaps from PIE *bhrekw- "to cram together," and thus related to frequens "crowded."
... for a farce is that in poetry which grotesque is in a picture. The persons and action of a farce are all unnatural, and the manners false, that is, inconsisting with the characters of mankind. [Dryden, "A Parallel of Poetry and Painting"]
According to OED and other sources, the pseudo-Latin farsia was applied 13c. in France and England to praise phrases inserted into liturgical formulae (for example between kyrie and eleison) at the principal festivals, then in Old French farce was extended to the impromptu buffoonery among actors that was a feature of religious stage plays. Generalized sense of "a ridiculous sham" is from 1690s in English.