Barnett also co-hosted the podcast Round Table of Gentlemen for Last Podcast Network, who confirmed the sad news via Twitter.
Comedy Central also tweeted about his passing, describing him as an "incredible comedian".
Saturday Night Live star Pete Davidson wrote a statement about Barnett, which was then posted to his friend Marcus Russell Price's Instagram Story.
"The world lost a great one today. One of our comedy family members Kevin Barnett has tragically passed. I love Kevin. I've known him for nearly 10 years and he's always been the sweetest and funniest," Davidson's note said. "Always had a smile on his face. Was one of the few that treated me like a comic even when I was just 16 years old. He always made me feel part of the group."
He concluded, "Thank you Kevin for being in my life and blessing us with your talents and positive energy. This one really f**ked me up. You will be missed."
Other former TV colleagues and friends took to Twitter to express their grief, including Chelsea Peretti, who stars in Brooklyn Nine-Nine.
