The ministry’s Department of Foreign Nationals and Refugees added that June 22 will be the last date on which Afghan nationals can participate in the census.
It also said that the census will not be extended.
Iran says nearly 5 million Afghan refugees are living in the country.
The latest refugee influx from Afghanistan happened last August following the Taliban takeover of the country.
Iran has repeatedly demanded the UN and also European countries assist it in hosting the Afghan refugees.
Tehran says it has yet to receive substantial help for this purpose.