The songwriter and guitarist was considered a pioneer of Argentine rock music, and his songs often touched on social themes.
Fellow musicians hailed Spinetta, nicknamed El Flaco or Skinny, as “one of the greatest poets of Argentine music”.
He died at home surrounded by his four children.
Fans and fellow musicians, including Argentina’s Charly Garcia and Cuba’s Silvio Rodriguez, posted tributes to Spinetta on social media websites.
The Argentine culture ministry, in a statement on its website, described him as “an exquisite poet” and a “complete autodidact in his musical training, deep reader of poetry and philosophy, jazz lover”.
Spinetta began in the 1960s with his band Almendra and later played with the bands Pescado Rabioso and Invisible.
He also had a solo career.
He announced last year that he had been diagnosed with lung cancer.