Hassan Khomeini, a 43-year-old cleric with close ties to reformists, was not verified as having sufficient religious competence by the Guardian Council, his son Ahmad said on his Instagram account, despite "testimony from dozens of religious authorities".
Khomeini had hoped to be a candidate for election to the Assembly of Experts, a powerful group of clerics which monitors the work of Iran's current supreme leader, Ayatollah Ali Khamenei, and will be responsible for selecting his successor.
Khamenei, now 76, took over from the elder Khomeini who died in 1989.
Elections to the 88-member Assembly and for parliament's 290 lawmakers will take place on February 26. Members of both bodies are elected in votes open to the general public.
However the 800 candidates for the Assembly first have to pass a vetting process conducted on behalf of the Guardian Council.
Khomeini, who would have been the first member of the family to take a prominent place in public office since his grandfather's death, was among hundreds of hopefuls excluded.
A spokesman for the Central Elections Supervising Committee, the vetting arm of the Guardian Council, said on state television that rejected candidates had until Saturday to lodge an appeal.
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Siamak Rah-Peyk said 166 candidates had been approved for the Assembly election, 111 were not authorised, 207 were disqualified and 58 had withdrawn.
The younger Khomeini has not been a prominent public figure but his candidacy had been contentious because of his connections to reformists, who have been hoping for a political comeback after long being sidelined.
The Guardian Council is dominated by conservatives and its role in picking who can run for office is contentious because of the deep divide between Iran's competing political factions.
Khomeini's son added on Instagram: "In my opinion, the reason for non-verification is clear to everyone."
On January 5, a member of the Guardian Council said Khomeini could be excluded from the elections because he did not attend an exam to certify his religious credentials.
However sources close to the cleric, who currently runs the mausoleum to the Islamic republic's founder in Tehran, later said there were other ways in which his religious knowledge could be verified.
At the time, a source close to Khomeini, who has ties to reformist former president Mohammad Khatami, told the official IRNA news agency he had not received any "invitation or text message" to go to the exam.
"At the time of examination, he was giving a lecture" on theology, the source said.
On Tuesday, Rah-Peyk said that 152 candidates had not attended the qualification exam.