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."
More top news
The 75-year-old comic book character has been named UN ambassador for the empowerment of women and girls.
The women have gone straight to the top of the charts with their new song, Shout Out To My Ex.
The country reflects after the two main presidential candidates tore into each other at a usually-civil and light-hearted charity event.