Bahrain, a Saudi ally, recalled its ambassador from Tehran on Monday due to the diplomatic row.
Saudi Arabia also cancelled all flights to and from Iran on Monday.
The protests occurred following the execution of prominent Shia cleric Nimr al-Nimr in Riyadh on Saturday.
Iran and Saudi Arabia are respectively the main Shiite and Sunni powers in the Middle East. Sudan and Bahrain, a tiny Sunni-led monarchy with a majority Shiite population, broke off ties with Iran hours after Saudi Arabia, while the United Arab Emirates and Kuwait downgraded theirs.
Before the breakdown, Iran and Bahrain maintained limited diplomatic relations. The Iranian charge d'affaires has been given 48 hours to leave the island nation. The United Arab Emirates announced shortly after Bahrain that it would downgrade diplomatic relations with Tehran and focus primarily on business ties.