There were no immediate details about how Hawkins died, with the band saying in a statement that his death was a "tragic and untimely loss".
Foo Fighters were on tour in South America. They played a festival in San Isidro, Argentina, on Sunday and had been scheduled to play at another in Bogota, Colombia on Friday night.
"His musical spirit and infectious laughter will live on with all of us forever," said a message on the band's official Twitter account.
"Our hearts go out to his wife, children and family, and we ask that their privacy be treated with the utmost respect in this unimaginably difficult time."
After Foo Fighters founder and front man Dave Grohl, Hawkins was probably the most prominent member of the group, appearing alongside Grohl in interviews and playing prominent roles in the band's videos.
He also starred in Foo Fighters' recently released horror-comedy film Studio 666 in which a demonic force in a house the band is staying in seizes Grohl and makes him murderous.
Hawkins and other members of the band - Pat Smear, Rami Jaffee, Chris Shiflett and Nate Mendel - are killed off one by one.
The film allowed the group, who for decades have been one of rock music's most durable acts, to have fun while acting out a long-running joke.
The film's premise came out of work on their 10th studio album at a home in Los Angeles' San Fernando Valley.
Hawkins was Foo Fighters' drummer for 25 of the band's 28 years of existence, taking over from original drummer William Goldsmith in 1997.
Born Oliver Taylor Hawkins in Fort Worth Texas in 1972, Hawkins was raised in Laguna Beach, California.
He played in the small Southern California band Sylvia before landing his first major gig as a drummer for Canadian singer Sass Jordan.
He spent the mid-1990s as the touring drummer for singer-songwriter Alanis Morissette before Grohl asked him to join the Foo Fighters.
It is the second time Grohl has experienced the death of a close bandmate. He was the drummer for Nirvana when Kurt Cobain died in 1994.
Hawkins is survived by his wife Alison and their three children.
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