Khodai was “one of the defenders of the shrines”, the semi-official Tasnim news agency reported.
The Israeli Prime Minister’s Office, which oversees intelligence agency Mossad, declined to comment on the events in Tehran.
“The sworn enemies of the holy system of the Islamic Republic of Iran once again showed their evil nature with the assassination and martyrdom of one of the members of the IRGC troops,” said Iranian Foreign Ministry spokesperson Saeed Khatibzadeh.
At least six Iranian scientists and academics have been killed or attacked since 2010, several of them by assailants riding motorcycles, in incidents believed to have targeted Iran’s disputed nuclear programme, which the West says is aimed at producing a bomb.
Israel has declined comment on such accusations.
In April, Iran’s intelligence ministry said it had arrested three Mossad spies in a statement published by the semi-official Fars news agency.
The “defenders of the shrines” also include Afghan and Pakistani volunteers.