Saudi Foreign Minister Adel al-Jubeir was speaking after demonstrators had stormed the Saudi embassy in Tehran.
Sheikh Nimr al-Nimr and 46 others were executed on Saturday after being convicted of terror-related offences.
Mr Jubeir said that all Iranian diplomats must leave Saudi Arabia within 48 hours.
Saudi Arabia was recalling its diplomats from Tehran, he said.
Mr Jubeir said Saudi Arabia would not let Iran undermine its security, accusing it of having "distributed weapons and planted terrorist cells in the region".
This is not a very good start to the new year All hell could easily break loose. Väinämöinen help us all.