The ministry said it expects voter turnout to be 70% and higher, by the vote's end. According to State media more than 45,000 polling stations were awaiting those looking to exercise their right to vote.
The elections, which kicked off at 8 am (03:30 GMT) will see hardliner President Mahmoud Ahmadinejad pitted against a pro-reform challenger more open to improving ties with the US.
The election is seen as a referendum on Ahmadinejad. His top opponent, Mir Hossein Mousavi, has energized many youth who want fewer hardline Islamic restrictions and better international relations.
There are about 46 million eligible voters in Iran, a country of 70 million people.
The other two candidates running are conservative Mohsen Rezaei and reformist Mahdi Karroubi.
Preliminary results are expected early on Saturday. If no clear winner emerges from Friday's vote, a run-off will be held on June 19 between the two front-runners.
"Voting for the 10th presidental election started throughout the country," State radio said, referring to the number of presidential polls held since the 1979 Islamic revolution.
Chavez wishes Ahmadinejad luck
Venezuela's socialist leader wished his hard-line Iranian counterpart good luck in his re-election bid in Iran's presidential ballot Friday.
Speaking to supporters Thursday, Hugo Chavez called Ahmadinejad "a courageous fighter for the Islamic Revolution, the defense of the Third World, and in the struggle against imperialism" - a reference to the US government's foreign policy.
Since taking office 10 years ago, Chavez has forged strong ties with Iran, raising concern in Washington. The two countries have increased cooperation in areas ranging from finance to factories. Iran now manufactures cars, tractors and bicycles in Venezuela.
Chavez also told his supporters that he refuses to join in international criticism of North Korea for conducting an underground nuclear explosion May 25, its first since a 2006 atomic test.
"They condemn. I don't. I don't allow myself to be pressured," Chavez said.
Dudi Cohen, the Associated Press and Reuters contributed to this report