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 Instagram. It did not state the reason for the termination.
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.
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.