Iran launched the "Shahab-3" missile, which has a range of more than 1000km.
The rocket was launched from the southern coast of the country and landed west of Tehran, CNN reporter Barbara Starr quoted the official as saying.
Starr added that the missile didn't pose a threat to shipping or US bases in the region, however, US intelligence assessed that Iran is attempting to improve the range and accuracy of the rockets.
The test came just hours after US Secretary of State Mike Pompeo said in a televised interview he would "happily" go to Iran for talks amid months of spiky relations between the two countries.
The official added that the US had been closely monitoring the test site prior to the missile’s launch.
The nuclear deal of 2015 does not prohibit the use of ballistic missiles, an omission cited by Trump as one of the reasons he pulled the US out of the deal last year.
Iran unveiled its newly developed surface-to-air ballistic missile with a 1,000km range in February, on the 40th anniversary of Islamic Revolution. The previous model had a range of 700km.
Amid spiralling tensions, Tehran maintains its missile tests are not in violation of its international agreements.
Iran has voluntarily limited the range of its missiles to 2,000 kilometres, but that is still enough to hit Israel and US bases in the Middle East.