The elite force said they also struck in Syria against the Islamic State.
"In response to the recent atrocities of the Zionist regime, causing the killing of commanders of the Guards and the Axis of Resistance ... one of the main Mossad espionage headquarters in Iraq's Kurdistan region was destroyed with ballistic missiles," the Guards said in a statement.
Israeli government officials could not immediately be reached for comment.
In addition to Monday night's strikes at northeast of Kurdistan's capital Erbil in a residential area near the US consulate, the Guards said they "fired a number of ballistic missiles in Syria and destroyed the perpetrators of terrorist operations" in Iran, including the Islamic State.
Iran's Revolutionary Guards said they fired a number of missiles at targets in Syria. (AP PHOTO)
Islamic State claimed responsibility for two explosions in Iran this month that killed nearly 100 people and wounded scores at a memorial for top commander Qassem Soleimani.
"We assure our nation that the Guards' offensive operations will continue until avenging the last drops of martyrs' blood," the Guards' statement said.
While recalling its envoy from Tehran, Iraq summoned Iran's charge d'affaires in Baghdad to protest against the strikes, the foreign ministry said. It said Baghdad would take all legal measures against what it called a violation of Iraq's sovereignty.
Since the October 7 rampage by Hamas fighters into Israeli territory and the ensuing Israeli bombing campaigns in Gaza and Lebanon, more than 130 fighters of Lebanon's Iran-backed Hezbollah have been killed in hostilities.
The US State Department condemned the attacks near Erbil, calling them "reckless", but officials said no US facilities were targeted and there were no US casualties.
"We will continue to assess the situation, but initial indications are that this was a reckless and imprecise set of strikes," Adrienne Watson, spokeswoman for the White House National Security Council, said in a statement.Â
Iraqi Kurdish Prime Minister Masrour Barzani condemned the attack on Erbil as a "crime against the Kurdish people".
At least four civilians were killed and six injured in the strikes, the Kurdistan government's security council said.
Multimillionaire Kurdish businessman Peshraw Dizayee and several members of his family were among the dead, killed when at least one rocket crashed into their home, Iraqi security and medical sources said.
Dizayee, who was close to the ruling Barzani clan, owned businesses that led major real estate projects in Kurdistan.
Additionally, one rocket had fallen on the house of a senior Kurdish intelligence official and another on a Kurdish intelligence centre and air traffic at Erbil airport was halted, the security sources said.
Iran has in the past carried out strikes in Iraq's Kurdistan region, saying the area is used as a staging ground for Iranian separatist groups as well as agents of its arch-foe Israel.
Baghdad has tried to address Iranian concerns over separatist groups in the region, moving to relocate some members as part of a security agreement reached with Tehran in 2023.
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