Radio presenter Tom Binns made the comments during a Christmas Day show on Birmingham radio station BRMB.
Binns then made a joke about the French royal family being beheaded and introduced the next song, Last Christmas by Wham!, with the words "from one Queen to another..."
"It's got to the point where comedians aren't allowed to say anything that could possibly offend anyone anymore," he added.
Binns said one listener sent him a message saying he should be sent to Iraq and hoped that he would be killed by a roadside bomb. "Other than that almost all the texts we received were in support of what I'd done."