"In response to the barbaric attacks on the Saudi Arabian Embassy in Tehran and its consulate in Mashhad ... the government of Sudan announces the immediate severing of ties with the Islamic Republic of Iran," a Foreign Ministry statement said.
Sudan has also decided to expel the Iranian ambassador, Saudi state television station Ekhbariya reported.
Similarly, the United Arab Emirates (UAE) announced it was downgrading diplomatic ties with Iran and limiting the number of Iranian diplomats in the country, state news agency WAM reported.
"The UAE has decided to reduce the level of diplomatic representation with the Islamic Republic of Iran to the level of a charge d'affaires and to reduce the number of Iranian diplomats in the country," WAM said.
Saudi Arabia cut ties with regional rival Iran on Sunday after Iranian protesters attacked its mission there, angered by the Sunni Muslim kingdom's decision to execute a leading Shi'ite cleric.