Saudi Arabia is reportedly planning to stop all flights to and from Iran and banning its citizens from travelling there.
The Saudi foreign minister Adel al-Jubeir told Reuters that all commercial ties between the countries would also be cut.
Sunni-led Saudi Arabia claims that the execution was part of a war on terrorism.
The foreign minister said that the leading Shiite cleric was a terrorist engaged in attacks adding that Riyadh should be applauded for the executions, not criticized
Saudi allies Bahrain, Sudan and United Arab Emirates have also cut or reduced diplomatic ties.
Saudi Arabia had earlier cut diplomatic ties with the Islamic Republic over the storming of its embassy in Tehran.
The break in the Iranian-Saudi relations followed the years of “Iran’s aggressive policies,” the minister told Reuters on Monday.
Iranian protesters set ablaze the Saudi Embassy in Tehran on Saturday night during a rally to condemn Riyadh’s execution of the prominent Shia cleric.
Nimr was among 47 prisoners beheaded or shot by firing squad across Saudi Arabia on Saturday, the largest number of individuals executed in the kingdom in a single day since 1980.