The 36-year-old criticised channel controller Peter Fincham for allegedly ordering his satirical song 'Woody Allen Jesus' be omitted from the chat show.
"Someone got nervous and sent the tape to ITV's director of television, Peter Fincham," he wrote on his blog. "And Peter Fincham demanded that I be cut from the show.
"He did this because he's scared of the ranty, s**t-stirring, right-wing press, and of the small minority of Brits who believe they have a right to go through life protected from anything that challenges them in any way."
Minchin went on: "It's hardly the end of the world. But I have to admit I'm really f**king disappointed. It's 2011. The appropriate reaction to people who think Jesus is a supernatural being is mild embarrassment, sighing tolerance and patient education."
Jonathan Ross defended Minchin on Twitter, writing: "Really gutted that the brilliant @timminchin song has been cut from my show," he wrote. "[The] decision was out of my hands."
However, ITV said the musical skit was "not right tonally" and "didn't quite work editorially", before adding in a statement to BBC News: "We often make changes to programmes before transmission."
Revealing what he thought of the lyrics, which light-heartedly describe Jesus as "short, Jewish and quite political", Minchin added: "It's not a particularly original idea, but it's quite cute. Being TV, I knew it would have to be gentle."
Watch Tim Minchin's 'Woody Allen Jesus' song below: