Notwithstanding any expansion of your question, seems like a qualified 'yes' is in order here. But thoroughly personality-driven satire of the type by Aretino won't be found until the late middle ages.

However, satire of morals and religion did exist. You could start with the 11-13th lyrics of various troubadours, but in particular Bertran de Born (this link is an awesome book), or Marcabru and Peire Cardenal. You could also look at the Carmina Burana dating from 12th and apparently produced by theological students. I know the former much better, but both corpuses have been written about at length so there are plenty of places to start with if you're interested; it really depends how deep you want to go. However, a sight reading of the works without context will probably be dissatisfying.

Some have argued for some of Peter Abelard's work as satirical, particularly his autobiography Historia Calamitatum, although it entirely depends on how one reads it. To me he was so smart (and so arrogant) that the satire is layered like a medieval exegesis. I would read Clanchy's biography Abelard:A Medieval Life for a very accessible introduction to his life and work.

all of the aforementioned texts are good examples, but if you want true satire of political, social, or religious satire, you can find it. i think there are elements of satire in abelard and dante, they are both so much more than mere satire.

the speculum stultorum is a satire on medieval society, for example. it's the story of a donkey who goes on a bunch of travels to become a human or learn to speak. i've translated the bit where he goes to the university of paris and the author satirizes the students and the priests in the city.

reynard the wolf (sometimes a fox) and ysengrim the fox were stock characters that were used to mock clergy at times.