While it wasn't active extortion the use of Indulgences in the medieval Catholic church comes close.

http://www.britannica.com/EBchecked/topic/286800/indulgence

Provides a very good overview and the last two paragraphs in particular are pretty telling. The wealthy who were known or confessed to have sinned were encouraged to provide monetary or material "penance" rather than the rather philosophical "10 hail marys" handed out to the poor in order to be granted absolution for whatever had taken place. It could and is by some seen as a form of extortion as at the time the fear of damnation was utterly real to most people and so many would sacrificed just about anything to avoid that fate.

Regarding actual extortion in terms of "Give me X or I'll tell everyone you did Y" there is plenty of anecdotal evidence that can be found through a simple Google search but little in the way of legitimate research or even well sourced stories of isolated incidents. Given the huge issues that the medieval Catholic church had with corruption it's almost certain that at least some isolated incidents took place but there's no evidence that it was a systematic issue and it was certainly never anything approaching church policy.