The ban will expire in October under the 2015 Iran nuclear deal.
It was formally known as the Joint Comprehensive Plan of Action.
Dian Djani, Permanent Representative of Indonesia to the UN and President of the council for August, announced the decision.
The envoy said China and Russia voted against the US-sponsored resolution.
Eleven countries, including the United Kingdom, France and Germany, abstained.
He said only two countries, “the U.S. itself and the Dominican Republic, voted in favour.”