As result of the sanctions, Americans will be prohibited from dealing with the companies, Al Hilal Exchange and Al Fida International General Trading, and other financial institutions risk losing access to the U.S. financial system for working with them.
The United Arab Emirates have previously revoked the license of the exchange firm.
Iran's currency, the rial, has plummeted due to international pressure, forcing banks to seek foreign currency.
Wednesday's sanctions come as Congress reevaluates its policy on Iran. Cohen and Wendy Sherman, under secretary for political affairs at the State Department, are appearing before committees in both the House and Senate to provide an update on the government's efforts against Iran.
In his prepared statement before the Senate Foreign Relations Committee, Cohen claimed that the sanctions "have heightened the economic pressure and imposed a very significant strain on the Iranian regime" and that the rial "has been hit hard."
In the last two years the currency has lost two-thirds of its value.
Cohen added, "The goal of our sanctions on Iran is to expose and impede the Iranian government’s continued pursuit of its nuclear and ballistic missile programs, and to help persuade the Iranian leadership that its only viable choice is to come into compliance with its international obligations."