Britain's National Cyber Security Centre and the Government Communications Headquarters, known as the GCHQ, are among the seven institutions listed.
Tehran said their actions "led to riots, violence and terrorist acts against the Iranian nation".
Iran has been rocked by protests since Amini, 22, died on September 16, three days after she was arrested by "morality police" in Tehran for allegedly breaching the country's strict dress code for women.
The street violence has led to dozens of deaths, mostly among protesters but also among the security troops, and hundreds of demonstrators have been arrested.
The 16 organisations and people were under sanctions for "their deliberate actions in supporting terrorism and terrorist groups, promoting and inciting terrorism, spreading violence and hatred, and violating human rights", Iran's Foreign Ministry said.
Protests rage on the streets of Tehran - in pictures
BBC Persian and Iran International, two Farsi-speaking channels based in the UK and considered "hostile" by Tehran, were also blacklisted.
Sanctions include a visa ban and the seizure of any "property and assets" in Iran.
Alternative Mahsa Amini protests - in pictures
The UK penalised the morality police and security officials on October 10.
The EU on Monday imposed sanctions on 11 Iranian people and four entities for the way in which they dealt with the month-long demonstrations.