The Bourne Legacy star was asked about the family during an interview with The Guardian and revealed that he is not a fan.
"Oh, all those ridiculous people with zero talent who spend their lives making sure everyone knows their name," he said. "Those stupid, stupid people."
Renner also insisted that he is not interested in celebrity, saying: "I know it's a cliché but I never wanted to be famous. I don't believe anybody wants to be famous."
50 Cent recently criticised Kim Kardashian when he was asked about her relationship with Kanye West, saying: "One man's trash is another man's treasure."
Jon Hamm also infamously criticised Kim Kardashian earlier this year when he claimed that "stupidity is certainly celebrated" in society, causing the reality star to describe his remarks as "careless".
Meanwhile, Kardashian's IMDB profile was hacked earlier this year, with the perpetrator changing her biography to say that she is "emblematic of the shallowness of American culture".