Giggs celebrated his 40th birthday on Friday and played a starring role as the Red Devils beat Bayer Leverkusen 5-0 in the Champions League earlier this week.
However, writing on Twitter, Barton claimed that although Giggs was a "vital" player for his club, his actions off the field were wrong.
"Giggs has done unbelievable to get to 40. Still a vital player for United. Some career he's had," he said.
"Still can't have him for getting up his brother's bird though. Great player but can't be doing that. No matter how much of a top player he is.
"Respect him as a player. But as a man, you do not do that to your own. He is a wrongun in my book."
It was revealed in 2011 that Giggs had reportedly had an eight-year affair with Natasha Giggs.