Following discussions between the club and the manager, "it was agreed that the conditions no longer existed between the parties to continue the professional relationship, particularly concerning the development of the sporting project," the statement said.
The 31-year-old Spaniard, who was previously assistant coach at Arsenal under Mikel Arteta, joined Parma in 2025, taking on his first senior managerial role on a two-year contract after replacing Cristian Chivu, now manager of Inter Milan.
"It has been an intense year and a half during which I gave my all, right up until the very last day, for a team and a club to which I have become deeply attached," Cuesta wrote on Instagram.
The decision came a week after Parma secured their first victory of the Serie A season, beating Genoa 2-1 at home. Parma are currently 15th in the Serie A standings after five rounds.
"We were a united family that fought until the very last minute to achieve what we always wanted: to win," Cuesta added.
Parma said Monday's training session would be led by the club's coaching staff pending further developments regarding the appointment of a new head coach.