The sanctions list, published in the bloc's official administrative gazette, also blacklisted the chiefs of the so-called morality police, the Revolutionary Guard's Basij paramilitary force, a uniformed branch of the national police, and officials in charge of those forces.
Iran vowed an 'immediate" response to the sanctions.
The 11 individuals and members of the four entities named in the sanctions are subject to EU visa bans and asset freezes.
Ahead of the blacklist's publication, German Foreign Minister Annalena Baerbock said of the "morality" police that it is a "word that is not really appropriate when you see the crimes that are being committed there".
The list was drawn up before the latest dramatic turn of events in Iran: a deadly fire at Tehran's notorious Evin prison, where the regime holds Iranian political prisoners, as well as dual nationals and foreigners.
The EU has been alarmed at the Iranian regime's bloody crackdown on protests sparked by the death a month ago of Amini, a 22-year-old taken into custody by morality police who arrest women deemed to wear Islamic headscarves inappropriately.
The demonstrations have since morphed into anti-regime street protests, with those taking part demanding the end of the mullah-led regime.
The sanctions list said the "morality" police and its Tehran and national chiefs were responsible for Amini's death.
"According to reliable reports and witnesses, she was brutally beaten and mistreated in custody, which led to her hospitalisation and to her death on 16 September 2022," it said.
The information and communications technology minister, Eisa Zarepour, was held responsible for internet blackouts imposed in Iran as the protests flared, curbing Iranians' access to information and freedom of opinion.
'Deaths of multiple people'
The Basij force was listed for its "particularly harsh" crackdown on protesters, "resulting in the deaths of multiple people". It is "directly responsible for serious human rights violations in Iran," the EU listing said.
Baerbock, arriving at an EU foreign ministers' meeting that adopted the sanctions, said the "we will not close our eyes" to the abuses being carried out in Iran.
She warned: "If this violence continues, then more (sanctions) will follow."
The United States, Britain and Canada have already announced their own sanctions against Iran for the rights violations taking place.
Tehran has responded by accusing the United States of fomenting the anti-regime protests.
Luxembourg's Foreign Minister Jean Asselborn was sceptical that the sanctions would "hurt" Iran.
But he said: "This regime may have worked during the last 40 years but it is not working now. And that is why the European Union has to take this first step."
The developments happened as hopes are fading of restoring the 2015 Iran nuclear deal that was torpedoed when then-president Donald Trump in 2018 withdraw US support.
The EU has over the past year and half been coordinating efforts, so far unsuccessfully, to bring the US and Iran back into full compliance with the accord, which aims to curb Iran's nuclear programme.
Dutch Foreign Minister Wopke Hoekstra said reviving the deal was important "but there's only one party blocking and stonewalling...in the last months and years -- and that is Iran itself".
Iran also fed into the ministers' discussion on Russia's war in Ukraine.
Kyiv and a growing number of observers say that Iran is supplying Russia with drones to strike Ukrainian targets, which Tehran denies.