Dusty Hill, the bassist in the American rock group ZZ Top, has died aged 72.

A statement on the band's Instagram account read: "We are saddened by the news today that our Compadre, Dusty Hill, has passed away in his sleep at home in Houston, TX.

"We, along with legions of ZZ Top fans around the world, will miss your steadfast presence, your good nature and enduring commitment to providing that monumental bottom to the 'Top'.

"We will forever be connected to that Blues Shuffle in C. You will be missed greatly, amigo. Frank & Billy."

Hill had taken a leave of absence from the band due to a hip problem just days earlier, NBC said.

The social media message was signed by the group's other members, drummer Frank Beard and guitarist Billy Gibbons.

The band was scheduled to perform in Simpsonville, South Carolina, on Wednesday, but a venue manager said the gig had been cancelled, according to NBC.

On Friday, the group announced that Hill, its "fearless" bass player, was "on a short detour back to Texas, to address a hip issue.

"They await a speedy recovery ... Per Dusty's request 'The show must go on!'

"With that directive, ZZ Top has put the services of Mr. Elwood Francis, their trusted guitar tech of the past two decades, into play with his slide guitar, bass guitar and harmonica playing in full swing."

Hill wasn't ZZ Top's original bass player, but he joined shortly before they recorded their debut album, ZZ Top's First Album, in 1971.

Throughout the 50 years since, the line-up stayed as just Hill, Gibbons, and Beard, making them one of the most stable acts in rock history.

Their big break came after a three-year hiatus during which Hill worked at an airport.

Reforming in 1979, they hit gold with 1983's Eliminator, the album that turned them into MTV stars.

The singles Sharp Dressed Man, Gimme All Your Lovin', and Legs are still staples of rock radio in the US.

Even though their recording success died away in the Nineties, the band never stopped touring and always maintained a huge following.

They were inducted into the Rock & Roll Hall of Fame in 2004 by Keith Richards.

Rock musicians, such as Whitesnake's David Coverdale, paid tribute, while Slash, of Guns'n'Roses, posted a picture of Hill, with the message "RIP Dusty Hill".