The vote would have failed if 35 percent of the population voted against the measure. However, less than 40 percent of the population participated in the referendum, according to provincial electoral data. Sixty percent of those who voted supported Casas' motion.
The opposition, part of President Mauricio Macri's Cambiemos (Let's Change) coalition, described the referendum's wording as "lax" and "unconstitutional".
Cambiemos and dissident Peronist leaders like Sergio Massa called on voters to "massively vote" for the "no option".
Last week, Justices Ricardo Lorenzetti, Horacio Rosatti and Elena Highton de Nolasco voted against the UCR Radical Party's appeal, which argued that Governor Casas should not be allowed to run for a third term in office.
Chief Justice Carlos Rosenkrantz voted in favour while Justice Carlos Maqueda was absent.