Police said a visitor to the cemetery in Nahlal in northern Israel discovered the graffiti, which called Dayan the "minister of failure" and was signed by "the fallen," Israel Radio said. The incident occurred just two days after a memorial service at the site.
"This always happens in October, the anniversary of the Yom Kippur War, and my father's death. ... I hope they find those who did it," Dayan's daughter told Army Radio.
"They don't even let the fallen rest in peace. This is outrageous. ... This is just evil," Ruth Dayan, Dayan's widow, told Ynetnews.com.
The Defense Ministry condemned the act and said it would repair the damage, Haaretz said.
Dayan, who died in 1981, served as Israel's fourth chief of staff (1953-58) and as defense minister during the 1967 Six Days War and 1973 Yom Kippur War. He also served in other ministerial positions.
He was held partially responsible for failing to recognize signs a war was brewing in the days before the Yom Kippur War. He also failed to fully mobilize Israeli troops in the first days of the war when Egyptian and Syrian forces inflicted heavy casualties on Israeli soldiers.