The club issued a brief statement on Sunday saying they had decided to part with the coach on Saturday evening after losing 3-1 at Valencia. It was the sixth defeat in seven league games.
Granada remained 17th, three points above 18th-placed Alaves.
"The club decided this Saturday to dismiss the first-team coach," said the statement. "We would like to thank Robert Moreno for his work and dedication during this period and we wish him all the luck in the future."
The club also suffered humiliation in the Spanish cup when it was eliminated by fourth-tier Atletico Mancha Real in December.
Ruben Torrecilla, the reserve team coach, takes over the first team on an interim basis.
Moreno, 44, joined Granada in June 2021 on a two-season contract.
The Catalan coach started as assistant to Luis Enrique at Roma, Celta Vigo, Barcelona and with Spain.
He acted as national coach for a few months in 2019 while Luis Enrique was sidelined for family reasons.
He coached Ligue 1 Monaco for the second half of the 2019-2020 season.