The 34-year-old, who retired from the game in 2011, set up the StandUp Foundation to help tackle homophobia and bullying within young people.
"I haven't had the pleasure of meeting Ben Cohen before but I'm delighted to remedy that serious deficit," Bercow said during a function, according to the Daily Mail.
"For those of you who aren't aware his background is as a rugby international, capped no fewer than 57 times for his country, and he is openly gay and has dedicated himself to fighting for gay rights."
After a few laughs from the crowd, Cohen shouted: "Don't tell my wife!", which prompted Bercow to apologise and backtrack on his comments.
Cohen also has two children with his wife Abigail.