In an announcement signalling it would reciprocate the unprecedented move, Tehran accused Washington of posing a "a major threat to regional and international stability and peace".
The decision to list the IRGC as a foreign terrorist organisation marked the first time the US has formally branded another country's military a terrorist group.
In an indignant response reported by state TV, Iran's Supreme National Security Council said: "This unwise and illegal measure is a major threat to regional and international stability and peace ... Iran labels the American regime as a supporter of terrorism."
Tensions between the two countries have mounted since Mr Trump pulled his country out of a 2015 nuclear deal with Tehran last May and reimposed sanctions that had crippled Iran's economy.
The US has already blacklisted dozens of people and entities with alleged connections to the IRGC, but had until now refrained from doing so to the entire organisation.
The designation imposes sanctions that include freezes on assets the IRCG may have in US jurisdictions and a ban on Americans doing business with it.
Mr Trump said: "This unprecedented step, led by the Department of State, recognises the reality that Iran is not only a state sponsor of terrorism, but that the IRGC actively participates in, finances, and promotes terrorism as a tool of statecraft."
In response, Iran's Supreme National Security Council said it has designated the United States Central Command (CENTCOM) and all its forces as terrorist and labelled the US a "supporter of terrorism".
The semi-official Fars news agency reported the statement after Iran's foreign minister said he wants to include the Middle East-based US military forces on his country's "terrorist groups" list.
The IRGC is a paramilitary organisation formed in the wake of Iran's 1979 Islamic Revolution to defend its clerically overseen government.
The force answers only to Iran's supreme leader, operates independently of the regular military and has vast economic interests across the country.
The new designation allows the US to deny entry to people found to have provided the Guard with material support or prosecute them for sanctions violations. That could include European and Asian companies and business people who deal with the Guard's many affiliates.
It will also complicate diplomacy. Without exclusions or waivers to the designation, US troops and diplomats could be barred from contact with Iraqi or Lebanese authorities who interact with Guard officials or surrogates.
The Pentagon and US intelligence agencies have raised concerns about the impact of the designation if the move does not allow contact with foreign officials who may have met with or communicated with Guard personnel.
Those concerns have in part dissuaded previous administrations from taking the step, which has been considered for more than a decade.
The state department currently designates 60 groups, such as al-Qaeda, Isis, Hezbollah and numerous militant Palestinian factions as "foreign terrorist organisations".
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