Levey said the US was urging other countries to "to deny financial assistance to Iran's nuclear and missile programmes", as supported by a recently passed UN Security Council resolution.
In addition to Bank Sepah, the Treasury order names Sepah International Plc, a wholly owned subsidiary of the bank in Britain and Bank Sepah's chairman and director, Ahmad Derakhshandeh, as weapons proliferators.
In Tehran, Iran's chief nuclear negotiator, Ali Larijani, told Iran's Student News Agency, ISNA: "This is not the first time that such measures of America take place and the bank harassments of America have happened in some cases, however these are not issues that can affect Iran's will."
The US action was taken under an executive order by the US president, George Bush, signed in June 2005 and is aimed at pressuring Iran into ending its nuclear activities.
Iran denies that it is seeking nuclear weapons and says its programme is for peaceful energy use only.
The Treasury claimed that Bank Sepah provides financial support and services to Iran's Aerospace Industries Organisation (AIO), as well as other groups which it said oversee Iran's missile programme.
The Treasury said in a statement: "Through its role as a financial conduit, Bank Sepah has facilitated Iran's international purchases of sensitive material for its missile programme."
It said Bank Sepah had financed a Chinese firm's sale of "missile-related items" to Iran in 2005.
The Treasury said that the AIO directed Bank Sepah in the same year to transfer over 500,000 dollars to a North Korean firm associated with Komid, a North Korean entity which the US says has provided Iran with missile technology.
The Treasury said the Iranian bank has more than 290 domestic branches.
The US government had similarly blacklisted another Iranian bank - Bank Saderat - in September, for its alleged "support for terrorism".