The graffiti called Dayan who led Israeli forces during 1967 six-day war and 1973 Yom Kippur as "minister of failure", the Haaretz daily reported quoting police.
The vandalisation of the grave, located near the northern city of Nazareth, came as Israel marked his 31st death anniversary and his daughter Yael Dayan dismissed it as an act of no consequence.
Dayan, who was Israel's long serving defence minister, died in 1981 of a heart attack.