Uruguayan Almada, who joined three-and-a-half years ago, led Pachuca to the CONCACAF Champions Cup title last year, sealing their place in the Club World Cup.
Pachuca also reached the FIFA Intercontinental Cup in December, where they lost to Real Madrid.
The manager bid an emotional farewell to players, staff and directors on Wednesday, Pachuca said in a statement, without giving a reason for his departure.
In March, FIFA said Liga MX sides Pachuca and Club Leon had failed to meet criteria on multi-club ownership and removed Leon from the Club World Cup.
The Court of Arbitration for Sport rejected Leon's appeal against the removal earlier this month.
Pachuca's spot in the 32-team Club World Cup, set to kick off in the U.S. on June 14th, was unaffected.
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