Muñiz was born in Guadalajara, Jalisco. Since early age, he showed musical talent, specifically as a romantic singer. He is the extraordinary lead voice of "Los Tres Ases" that rivaled "Los Panchos".
Muñiz's first album was a tribute to singers of other eras. It was titled "Aquellas Canciones!" ("Those Songs!"), and it was released in 1956. That was the first of close to 80 albums, all of which he recorded under the BMG or RCA Internacional labels.
His extensive solo career includes top 40 hit chart singles all over Latin America such as "Voy a Cambiar Mi Corazon" by singer/composer Miguel Poventud. He is an international artist with fans in Brasil and Poland.
In 1965, he began an uninterrupted streak of years traveling to Puerto Rico's Caribe Hilton Hotel in San Juan around Christmas, to offer concerts there (at one time, Muñiz claimed he was such a regular at the hotel that could figure out his way out of any of the hotel's suites and out of the facility blindfolded). This lasted close to thirty years. Muñiz has since returned for yearly shows at the Caribe Hilton, this time around Mother's Day.
In 1967 he was playing a hotel nightclub in Caracas, Venezuela, and left the facility during one of his breaks. A bomb exploded at the nightclub, demolishing the stage and killing various musicians. Muñiz escaped unharmed.
He has also performed at large stadiums and coliseums throughout his career with prominent Latin artists in the United States and Latin America.
Among the albums recorded by Muñiz are Marco Antonio Muñiz con Los Trovadores del Caribe (Marco Antonio Muñiz with Los Trovadores del Caribe) which was his fourth album, Mi Novia es Guadalajara! (Guadalajara is my Girlfriend!), which was his fifth, Salsa a la Manera de... (Salsa, Marco Antonio's Way..., which represented his first foray into the Salsa rhythm), 1991's Mi Borinquen Querido (My Dear Borinquen, where he paid homage to Puerto Rican folklore music), a 1993 dedication to Pedro Infante, and a 1997 album and CD which was dedicated to Jose Alfredo Jimenez.
Apart from his multiple albums and concerts, Muniz has also appeared numerously on television shows across Latin America, but, especially, in his native Mexico and his beloved Puerto Rico.
His son, "Jorge "Coque" Muñiz" is also a Mexican entertainment personality, as a show host and comedian at various Televisa television shows.