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State television showed images of the sand coloured Qiam (Rising) blasting into the air from a desert terrain, amid chants of "Allahu Akbar" (God is greatest).
The words "Ya Mahdi" were written on the side of the missile, referring to Imam Mahdi, one of the 12 imams of Shiite Islam, who disappeared as a boy and whom the faithful believe will return one day to bring redemption to mankind.
Vahidi, whose speech during Friday prayers in Tehran was broadcast on television, did not say when the launch took place nor did he reveal the precise range of the missile.
Fars news agency had in a report earlier this week quoted the minister as saying that Qiam was a short-range missile.
"The missile has new technical aspects and has a unique tactical capacity," he said on Friday, adding that the device was of a "new class."
"Since the surface-to-surface missile has no wings, it has lot of tactical power, which also reduces the chances of it being intercepted," he said.
Iran's ISNA news agency cited Vahidi as saying that Qiam was entirely designed and built domestically and was powered by liquid fuel.
"This missile is capable of hitting the target with high precision," Vahidi said.
On Tuesday, Vahidi had said that Qiam was to be test fired during the annual government week, the period when Tehran touts its achievements in various fields. This year government week begins on Monday.
The third generation Fateh 110 (Conqueror) missile was also to be test fired during this period. Iran has previously paraded a version of Fateh 110 which has a travel range of 150 to 200 kilometres (90 to 125 miles).
Also during government week, the production lines of two missile-carrying speedboats, Seraj (Lamp) and Zolfaqar (named after Shiite Imam Ali's sword) are due to be inaugurated, while a long-range drone, Karar, is expected to be unveiled.