China and Singapore did not receive such waivers, putting pressure on Iran's top oil buyer and a major blender of the country's fuel oil, respectively.
South Africa, Taiwan, Malaysia and Sri Lanka will also be exempted from the sanctions, Clinton said.
The sanctions, which the United States may impose starting June 28, aim to strangle Iran's nuclear program by cutting funding from its oil industry. The United States and the European Union believe Iran is trying to build nuclear weapons. Tehran says the program is strictly for civilian purposes.
"By reducing Iran's oil sales, we are sending a decisive message to Iran's leaders: until they take concrete actions to satisfy the concerns of the international community, they will continue to face increasing isolation and pressure," Clinton said in a release.
Banks and other institutions in the economies that received waivers will be given a six-month break from the threat of being cut off from the U.S. financial system under sanctions signed late last year by President Barack Obama.
Although China did not immediately receive a waiver, it does not necessarily follow that the United States will impose sanctions on the country from June 28.
It was not immediately clear why China failed to get the exemption. However, backers of tough sanctions on Tehran believe China has received clandestine cargoes of oil from Iran, which has disabled tracking devices on some of its shipments.
In March, the United States granted exceptions to Japan and 10 EU countries for significantly cutting purchases of Iranian petroleum.