The 43-year-old former Racing Club coach, who took charge a year ago, saw his team go down 4-1 to Cruz Azul on Saturday and 3-0 to Santos Laguna last weekend.
"Yesterday, after the meeting between Cruz Azul and Pachuca, Guillermo Rivarola presented his resignation to the technical director, deciding to take a step aside," the club board said in a statement.
Pachuca, who will play in the Club World Cup in Abu Dhabi in December, have taken four points from four matches in the Apertura and lie third in Group Two, a point behind leaders America, who were held 1-1 by Atlas at the Azteca.
Title holders Toluca are struggling in fourth place in Group Two with three points after a 1-1 draw with Tigres UANL.
In Group One Santos Laguna beat Chiapas Jaguares 1-0 and lead the group with a perfect record of 12 points from four matches. They are two points ahead of Monterrey, who crushed Pumas UNAM 5-2 on Saturday.
Guadalajara, fifth with four points from two games in Group One, had their derby against Estudiantes UAG postponed. They have travelled to Brazil for Wednesday's second leg of the Libertadores Cup final against Internacional in Porto Alegre. Inter won the first leg 2-1.
Cruz Azul lead Group Three with nine points, one more than unbeaten Puebla, who drew 1-1 at home to Atlante.
