The Austrian president has a mostly ceremonial role and after a call by the conservative People's Party, which decided against fielding a candidate, to cast a blank ballot, turnout was expected to be low.
Fischer, 71, is known for his caution and diplomacy and held various leadership positions in his party and in parliament before winning the presidency on April 25, 2004.
Rosenkranz, on the other hand, has caused controversy for suggesting that Austria's law banning the glorification of the Nazis is not in line with the country's constitution and hinders freedom of expression.
She recently formally declared support for the law after pressure from the publisher of the country's most widely read newspaper.
The 51-year-old mother of 10, whose husband was part of a far-right political party that was banned for being too radical, said her comments on the country's anti-Nazi law were misinterpreted by her critics and the media.
"Of course I condemn the monstrous atrocities. I've never done anything else,'' Rosenkranz told The Associated Press news agency, in reference to the mass
killings of Jews and others by the Nazis.
A recent opinion poll published by the magazine Profil gave Fischer 82 per cent, followed by 13 per cent for Rosenkranz and five per cent for Gehring.
Some analysts say Rosenkranz could win up to 20 per cent amid low voter turnout and a larger than normal number of invalid ballots.
The elections are being watched as a yardstick of far-fight sentiment in the country.
Polls will close at 1500 GMT.