Estudiantes Tecos hosts America, Pachuca receives Puebla, Atlante takes on Atlas and Cruz Azul plays Jaguares.
The games will be played over March 12, 13 and 14 and will be decided over just one match, with extra time and penalties resulting in case of a draw.
In last season’s quarterfinals, second division teams made up half of the places and knocked out the Liga MX teams in each of the four ties.
This Clausura, there are a couple of Mexico’s biggest clubs looking to pick up a trophy via the Copa MX, most notably America and Cruz Azul.
America hasn’t won a trophy since 2006, while Cruz Azul’s wait extends back to 1997.
The reigning Copa MX champion is Cuauhtemoc Blanco’s Dorados de Sinaloa, who defeated Correcaminos in last season’s final.
Mexico’s domestic cup competition was resurrected in the Apertura 2012 for the first time since 1997.