Sepanta Niknam, a member of Iran's ancient Zoroastrian religion, was the only non-Muslim elected to the council in the central city of Yazd in May.
But "an individual made a complaint to the administrative tribunal and the participation of this councillor has been suspended until a decision has been made", the president of the council, Gholam-Ali Sefid, told AFP.
Sefid said he was working with local officials to have the complaint thrown out.
It follows a ruling earlier this year by Ayatollah Ahmad Jannati, head of Iran's Guardian Council, which oversees elections, saying that religious minorities were barred from standing in municipal polls.
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Because the Guardian Council has power only over national elections, the ruling was rejected by parliament, but that does not appear to have prevented the complaint against Niknam.
The controversy comes despite the fact that Iran officially recognises "Iranian Zoroastrians, Jews and Christians" as religious minorities.
Parliament has several religious minority members, including three Christians, a Zoroastrian and a Jew among its 290 deputies.
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