The action is meant to enforce European Union sanctions, as global financial transactions are impossible without using SWIFT, and will go a long way toward isolating Iran financially.
The Society for Worldwide Interbank Financial Telecommunication, or SWIFT, is a banking hub crucial to oil, financial transactions and other trades.
Because of its reach, SWIFT's decision to cut off some 30 Iranian banks and subsidiaries could hinder not only banking but also the country's lucrative crude oil industry and possibly hurt Iranian households that depend on remittances from relatives living abroad.
"Disconnecting banks is an extraordinary and unprecedented step for SWIFT," said Lazaro Campos, chief executive of the company. "It is a direct result of international and multilateral action to intensify financial sanctions against Iran."
In a statement, the company said the EU decision to impose sanctions "prohibits companies such as SWIFT to continue to provide specialized financial messaging services to EU-sanctioned banks" and "forces SWIFT to take action."
There was no immediate reaction from the Iranian government or the banks involved. Not all Iranian banks are subject to EU sanctions.
Though Thursday's move adds no new sanctions, it is intended to maximize the impact of the EU sanctions that have already been approved.
"It's tightening the noose," said Ali Ansari, an expert on the Middle East at the London-based Chatham House think tank.
"I think it will just reinforce what's already been happening." And that, he said, is increasing isolation and difficulty in conducting trade and commerce.
In a statement, the European Council - comprised of the government leaders of the 27 European Union countries - said it had "developed the application" of its restrictive measures against Iran.
"In this context, the Council agreed that no specialized financial messaging shall be provided to those persons and entities subject to an asset freeze," the statement said.
The EU sanctions are aimed at forcing Iran to demonstrate to the international community that it is not trying to develop nuclear weapons. Iran says that its nuclear program is for peaceful purposes only, but officials in many other countries - including Israel - believe otherwise.
SWIFT and similar services facilitate not only large financial transactions, but small ones as well, raising the question of whether the EU directive could have unintended consequences. Numerous Iranians, including opponents of the current regime, live abroad and many may use these financial transaction services to send small amounts of money to their families back home on a regular basis.