The Mexican-American singer died on Friday in San Antonio from health complications, according to his daughter, Aubry Rodriguez.
She also shared a statement on social media saying he went peacefully and was surrounded by family.
"Dad was not only a legendary musician whose artistry touched millions around the world, but also a deeply loved husband, father, uncle, and brother whose warmth, humour, and compassion shaped the lives of all who knew him," she wrote.
Rodriguez was named the most promising male vocalist at the 1972 Academy of Country Music Awards, and his debut, Introducing Johnny Rodriguez, was nominated for album of the year in 1973.
More than a dozen of his albums and singles landed in the top 10.
Rodriguez later said his career suffered after he began to use drugs and alcohol excessively.
Rodriguez was born in Sabinal, Texas, a small town about 145km east of the US-Mexico border.
A Texas jury acquitted Rodriguez of murder in 1999, about a year after he walked into his mother's house in Sabinal and shot once at an acquaintance whom he thought was a burglar.
Israel Borrego, 26, died a day after he was shot.
Rodriguez continued to play concerts in South Texas and was inducted into the Texas Country Music Hall of Fame in 2007.
