The election comes a day after Egypt's Supreme Constitutional Court dissolved Parliament and ruled the former Mubarak regime prime minister, Ahmed Shafiq, had a right to run in the presidential runoff vote.
The court rejected a law that would have removed Shafiq from the race, BikyaMasr.com reported.
Shafiq is facing Muslim Brotherhood candidate Mohamed Morsi, who has the support of Islamic groups in the country.
Morsi backers urged people to vote for him to prevent "death of the revolution," BikyaMasr.com said.
Some Egyptians, including many from revolutionary groups and coalitions, were expected to boycott the election or void their votes.
More than 400,000 soldiers have been deployed around voting places by the military ruling council to prevent clashes.