I can't attest to what I've encountered being the earliest, but my period of study (English Civil War) was significantly affected by the boom in printing and the drop in restrictions on publishing so I feel it'd be a strong starting point for the discussion in a 'rise of mass media' sort of a way.
The text that I've found before that best seems to fit the bill was Jordan, Thomas, A diurnall of dangers. VVherein are manifested and brought to light, many great and unheard-of discoveries. To the admiration of all who have eares to heare, or strong hearts to endure. Found out and published in the yeare of just jealousies, apparant plots, fatall feares, and single securities, London, 1642., (British Library Thomason E.112) which is full of comically dim Royalists, cannon stealing shenanigans and the attempted theft of a lion from the Tower of London, oh and also tells us that some of the lions were sick poor things :( ‘one is troubled with a chincough, and the other lies sick of the tooth-ache’.
Really though you'd be better looking at Hughes, Ann, Gangraena and the Struggle for the English Revolution, Oxford, 2004. for a more definite and less specific answer, she covers a lot more of the general literature of the period, within its type and applicability to Gangrarna of course, where as my focus was particularly on the Tower.
Or of course someone may have other info that hugely predates me!
This postdates /u/e-weatherwax's example by quite a bit, but there was a little-known fad phenomenon of amateur newspapers, distributed by mail, in the 1870s to 1890s in the U.S., some of which were of a satirical-news nature.
The whole phenom was called "Amateurdom." Many, but not all, of the publishers were adolescent boys.
Jessica Isaac has studied and written about this phenomenon in various venues. Check out her website at www.jessicaisaac.net. And there are various organizations that collect and study these publications, one of which is called "The Fossils"; they are involved in (and Isaac is speaking at) an Amateur Journalism Conference in Madison, Wis., in July: https://www.library.wisc.edu/friends/aj/
This also postdates the English Civil War example, but Ben Franklin was a frequent writer of political satire (usually combining humor with a political message), often in the form of fictitious news or fanciful proposals.
Two examples of his work are:
Felons for Rattlesnakes (1751)written in response to a proposal to send British felons to the colonies. Franklin response that the colonies should reciprocate by sending a ship full of rattlesnakes back to England. Noting that the climate might improve their temperament (an argument that the British used to justify sending felons to the Colonies), and that unlike a felon a rattlesnake will at least warn you before it strikes.
An edict from the king of Prussia (1773) In which the "king" (under the justification that England was once part of Prussia) proposes that England should be taxed and ruled from afar, paralleling arguments that the British Parliament was using to justify its control of the American colonies.