Also sacked on Thursday were former Ecuador captain Alex Aguinaga at San Luis and ex-Mexico international Benjamin Galindo at Santos Laguna.
"Hugo Sanchez is no longer coach... We thank him for his commitment, professionalism and image... He has been offered a part in the Pachuca Group's future projects," a Pachuca statement said.
Former Real Madrid and Mexico striker Sanchez, who in May signed a contract until the end of the season, steered Pachuca to 13th place in the league phase of the championship.
The top eight after the 17-match league qualified for the knockout rounds.
Sanchez has been replaced by Argentine-born former Mexico forward Gabriel Caballero, who played for Pachuca and was being groomed to take charge of the team, the statement added.
San Luis came under new ownership this week and the club's authorities opted to sack Aguinaga, who presided over three wins and four draws in 11 matches during the league phase where they finished 15th.
Aguinaga had been signed as the club's sporting director at the beginning of the season but took over as manager when he sacked coach Jose Luis Trejo after six matches.
Galindo had been at Santos Laguna since mid-2011 and has lost his job despite steering them to the Clausura title last May. His team just missed out on a berth in the quarter-finals with ninth place in the league standings.
There was also a leading player transfer on Thursday with Argentine former Derby County and Cruz Azul striker Emanuel Villa moving from Pumas UNAM to UANL Tigres.
Toluca, Tijuana, America and Cruz Azul are favourites to reach the semi-finals after winning the first legs of their first knockout round ties.
The second legs this weekend include Tijuana at home to Monterrey with a 1-0 lead in a clash of northern teams.
Toluca host troubled Guadalajara, who they beat 2-1 at the Chivas' Omnilife stadium on Thursday where club owner Jorge Vergara was involved in a slanging match with fans who insulted him over the team's poor form.
Guadalajara fans are impatient with the apparent lack of improvement after nearly a year under Dutch duo Johan Cruyff, Vergara's consultant, and coach John van't Schip.
America are at home to Morelia at the Azteca in Mexico City with a 2-0 advantage and Cruz Azul defend a 2-1 lead at promoted Leon.