"There are no words to express my feelings and the love I have for my brother. Our family will miss him. But I know he's in a better place," Ronald Isley said in a statement released on Thursday by an Isley Brothers publicist.
Further details were not immediately available.
A Cincinnati native, Rudolph Isley began singing in church with brothers Ronald and O'Kelly (another sibling, Vernon, died at 13) and was still in his teens when they broke through in the late 1950s with Shout, a secularised gospel rave that was later immortalised during the toga party scene in Animal House.
The Isleys scored again in the early 1960s with the equally spirited Twist And Shout, which the Beatles liked so much they used it as the closing song on their debut album and opened with it for their famed 1965 concert at Shea Stadium.
The Isleys' other hits included This Old Heart Of Mine (Is Weak For You), later covered by Rod Stewart, and the Grammy-winning It's Your Thing.
In the 1970s, after younger brother Ernest and Marvin joined the group, they had even greater success with such singles as That Lady and Fight The Power (Part 1) and such million-selling albums as The Heat Is On and Go For Your Guns.
Rudolph Isley left the group in 1989, three years after the sudden death of O'Kelly Isley, to become a Christian minister.
He was among the Isleys inducted into the Rock and Roll Hall of Fame in 1992.
