Price has complained to Ofcom about the joke, and they have launched an investigation.
Channel 4's head of comedy Shane Allen stated: "We are aware that Frankie Boyle's comedy can be very challenging which is why we have gone to careful lengths in scrutinising the material editorially, in scheduling the series appropriately and by giving clear and strong warnings into each of the programmes.
"We think that it is important that a space on terrestrial TV exists for comedy that takes risks and pushes boundaries and we stand by our original decision to broadcast the programme."
Price has responded by saying: "They are saying it is okay to ridicule people - even children - for disability in a way they would not dare over race or sexual orientation. The people who control the channel are endorsing this behaviour and it is disgusting. Even the fact that Ofcom are investigating the first broadcast has not made them divert from this path.
"This issue is not about me, other than Harvey is my son. This issue is about discrimination."