Sergei Bagapsh, the incumbent president, is running for a second term against rivals who include Raul Khadzimba, a former vice-president and ex-KGB agent, and Beslan Boutba, a businessman.
Tbilisi rejects vote
Georgia has called the election a "comedy" supported by Russia, which has thousands of soldiers in the territory.
Semyon Grigoryev, Russia's ambassador to Abkhazia, said on Friday he was confident that the vote in the contested region would go smoothly. Officially, the West will ignore it.
Abkhazia, which broke away from Georgia in 1993 after a 13-month war, is considered to be a flashpoint for further unrest between Russia and Georgia in the South Caucasus.
The political opposition in Abkhazia has suggested that there could be irregularities in the vote, which comes five years after a presidential election in late 2004 which saw Khadzimba challenge a result that was in Bagapsh's favour.
Moscow has not said who would it prefer to win the vote, which some analysts have said could go to a run-off between Bagapsh and Khadzimba.
Russian ties questioned
Bagapsh has won support from some Abkhaz after winning Russia's recognition of the territory as an independent state during his rule.
Khadzimba has tried to appeal to those who say that Bagapsh has given too much influence in Abkhaz affairs to Russia.
"We are all talking about strengthening ties with Russia, but we also state strongly that we must preserve our dignity, defend our position, and not create some kind of amorphous space without rights or responsibility," he said.
Abkhazia and South Ossetia, another breakaway region in Georgia, rejected Tbilisi's rule soon after the break-up of the Soviet Union in 1991.
In Augugst 2008, Georgia launched an assault on South Ossetia that brought a counter-strike by Russian forces. Abkhazia took back its last enclave held by Georgia during the conflict.
About 3,600 Russian soldiers are deployed in Abkhazia, where two Russia military bases are under construction.
Nicaragua and Venezuela are the only countries aprt from Russia that recognise Abkhazia as an independent state.