Kluivert's departure follows Indonesia's "devastating" loss on Sunday in Jeddah against Iraq, ending their chances to qualify for next year's World Cup in the United States.
"After an open, full and respectful discussion, both parties agreed to end this partnership," the federation said on its website.
"The termination of this collaboration was made by mutual agreement, taking into account internal dynamics and the strategic direction of the national team's future development," the PSSI continued.
Indonesia were looking to qualify for the World Cup for the first time since the country claimed independence from the Netherlands in 1945, and their progress to the fourth round of Asia's preliminaries was the country's best performance to date.
Dutch-Indonesian stars
Former AC Milan, Ajax and Barcelona player Kluivert was hired in January, with his contract set to expire next year. He oversaw a team built largely on players from the country's Dutch diaspora, stemming from a policy introduced in 2023.
Ever since, 14 Dutch football players with Indonesian heritage have represented the Southeast Asian island nation, among whom is captain Jay Idzes.
"The PSSI expressed its appreciation for the contributions of all members of the coaching team during their tenure. This step was taken as part of a comprehensive evaluation of the national football coaching and development program," the federation concluded.
