The presenter was on holiday at Black's home in Barbados when he slipped over and cracked his nose, The People says.
Black took him to hospital for treatment but he has now returned to the UK.
Speaking on his Radio 2 show, O'Grady joked: "It was in the morning and I wasn't drunk, before you start. Now I look like W. C. Fields. No more glamour modelling for me. I've got to have a nose job done."
He continued: "There was me and Cilla Black in a hospital in Barbados that resembled a hut in Tenko. She had on an old-fashioned shirt and flip-flops with her hair on end and no makeup. I had a torn shirt with a wodge of toilet paper rammed under me nose.
"We looked like something out of Shameless."
O'Grady will launch a Friday night chatshow on ITV1 later this year.