Iran's application, as well as that of the United Arab Emirates as a founder-member, was approved by other founding members, according to a statement from the ministry on Tuesday.
So far, more than 50 countries have applied for membership of the bank, to which China pledged to provide $50 billion in initial capital.
Turkey announced on March 26 that it had applied for the membership of the bank, which aims to have more than $100 billion in initial capital and is expected to start operations at the end of 2015.
The U.S. and Japan have not applied for the membership of the bank as the U.S. has made clear it treats China's motives as suspicious.
Chinese officials said a total of 35 countries had been admitted to membership as they fulfilled procedures.
China had previously announced that founding members would be determined by April 15.
Governments applying for founding membership include China, Bangladesh, Cambodia, India, Indonesia, Kazakhstan, Kuwait, Malaysia, Maldives, Mongolia, Myanmar, Nepal, New Zeeland, Oman, Pakistan, Philippines, Brunei, Laos, Thailand, Saudi Arabia, Singapore, Sri Lanka, Tajikistan, Uzbekistan, Vietnam, Qatar, Jordan, UK, Germany, France, Italy, Australia, South Korea, Denmark, Austria, Switzerland, Russia, Turkey, Luxembourg, Israel, Iran, Taiwan and the United Arab Emirates.