The Texas-born musician died on Friday night, reports said.
His band confirmed Paul’s death in a post on their social media accounts, and did not release further details.
It said: “Vincent Paul Abbott aka Vinnie Paul has passed away.
“Paul is best known for his work as the drummer in the bands Pantera and Hellyeah. No further details are available at this time.
“The family requests you please respect their privacy during this time.”
Pantera released several albums during the 80s and 90s.
Their best-selling album, Vulgar Display Of Power, went multi-platinum and was one of the most influential heavy metal albums of the 1990s, selling more than two million copies.
The album “was a near-perfect example of what would come to be known as groove metal and a blueprint for how heavy music sounded throughout the Nineties and beyond,” Rolling Stone magazine wrote.
People from the music industry have been paying their tributes.
Gene Simmons from KISS tweeted: “Rest in peace, Vinnie. Our prayers and good wishes go to his family, friends and fans.”
Black Veil Brides drummer Christian “CC” Coma said: “I have just heard about the legend Vinnie Paul’s passing.
“I am beyond gutted about this as he welcomed me with open arms early in my musical career.
“Thank you for so many great memories and so many legendary songs. You will be truly missed.”
Vinnie Paul formed Pantera in 1981 with his brother “Dimebag” Darrell Abbott, and the band went on to win Grammy nominations before dissolving.
Darrell Abbott died in 2004 after being shot on stage during a concert.
He was playing his set with Damageplan, another band he founded with Paul, when he was shot five times in the head by a former marine in the crowd.
David Mustaine of Megadeth tweeted: “I just woke up in Belgium to the news that my friend Vinnie Paul has passed away. Another metal hero taken too soon. Say hello to Daryl for me. Rest In Peace, my dear friend.”
Sebastian Bach, frontman of Skid Row, tweeted an emotional tribute.
“Rock in peace Vinnie Paul,” he wrote, along with a video of him crying and saying “it’s horrible”.
“I loved you Vinnie and you were such a good guy and so nice to me.”