Army radio warned that militants would try to infiltrate Israeli settlements in the West Bank and the Gaza Strip.
As was the case in previous years, the army has imposed a full closure on Palestinian areas. It will last until Tuesday morning.
So far only a number of minor incidents have marred the holiday.
Yom Kippur, the day of atonement, is celebrated by Israel and Jews around the world for 24 hours - starting at sundown on Sunday.
Curfews
Palestinian workers and businessmen are not allowed to leave the West Bank and Gaza, and border crossings to Egypt and Jordan have been closed.
An Israeli military spokesman said the imposition of curfew was justified in view of the heightened risk of attacks by militants.
Although curfews remain in force in Palestinian towns, there have been some breaches of the security regime.
Despite a 12th straight day of curfew in Nablus, around 200 Palestinians marched through the city in protest at the setting up of a new checkpoint which they say has severely hampered traffic in the city.
Witnesses said the Israeli army did not try to stop the march, which passed off peacefully.
However in nearby Tulkarm, an Israeli helicopter reportedly suffered minor damage after shots were fired at it.
And in Jenin one Palestinian man was wounded in clashes with Israeli troops.
Meanwhile Palestinian sources in Gaza said a 28-year-old woman was wounded by Israeli fire during a brief incursion in the town of Rafah, on the border with Egypt.