"This deliberate action by Saudi Arabia is a violation of all international conventions that protect diplomatic missions," foreign ministry spokesman Hossein Jaber Ansari was quoted as saying by state television.
"The Saudi government is responsible for the damage caused and for the situation of members of staff who were injured," Ansari added, without specifying when the alleged strike took place.
"The Islamic republic reserves the right to pursue its interests in this matter," he said.
Nimr's death sparked demonstrations in many countries including Iran, where protesters stormed and set fire to the Saudi embassy in Tehran as well as the kingdom's consulate in second city Mashhad.
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Riyadh cut ties with Tehran in response and was joined by some of its Sunni Arab allies including Bahrain and Sudan. The United Arab Emirates also downgraded relations with Iran while Kuwait and Qatar recalled their ambassadors.
Also today, Iran banned all products from Saudi Arabia and said a ban on Iranians travelling to the Saudi holy city of Mecca for the umrah pilgrimage would remain in place "until further notice".
"The cabinet has banned the entry of all Saudi products and products from Saudi Arabia," a government statement said.