The travel advisory comes as Iran is threatening to attack Israeli targets following the assassination of its top nuclear scientist last Friday.
Iran accuses Israel of being behind the attack. Israel has not commented.
Israel in recent months has signed agreements establishing diplomatic relations with the UAE and Bahrain.
The agreements, brokered by the Trump administration, have generated widespread excitement in Israel and thousands of Israeli tourists are scheduled to travel to the Gulf this month.
"In light of the threats heard recently by Iranian officials and in light of the involvement in the past of Iranian officials in terror attacks in various countries, there is a concern that Iran will try to act in this way against Israeli targets," said a statement issued by the prime minister’s National Security Council.
It also advised against travel to Georgia, Azerbaijan, Turkey, the Kurdish area of Iraq and Africa.
Iran and its proxies have targeted Israeli tourists and Jewish communities in the past.
Hezbollah agents bombed a bus carrying Israeli tourists in Burgas, Bulgaria, in 2012, killing six and wounding dozens.
That year, Israel also accused Iran of being behind attacks targeting Israeli diplomats in Thailand and India.
Iran and Hezbollah also bombed the Israeli Embassy and Jewish community center in Buenos Aires in 1992 and 1994, claiming the lives of scores of civilians.
Concerns for the safety of Israelis in Dubai also is not without precedent.
In 2000, an Israeli ex-colonel was kidnapped by Iranian proxy Hezbollah and held captive in Lebanon until he was released in a prisoner exchange in 2004.