On his LBC 97.3 phone-in show, Mr Clegg said: "I was just dismayed and incredibly surprised to hear this still goes on in this day and age.
"I find it so out of step with everything else that's happening in the rest of society. It just seems so old fashioned and so anachronistic to just have a golf club saying that just because you are a woman you can't be a member of that club.
"I think many people will just shake their head and say 'how on earth is this still possible in this day and age?'."
He added: "I'm dismayed the club does not accept women as members. I find that inexplicable in this day and age, I really do."