Sergei Bagapsh, the incumbent president, ran for a second term against rivals who include Raul Khadzimba, a former vice-president and ex-KGB agent, and Beslan Boutba, a businessman.
'Russia supported comedy'
Georgia has called the election a "comedy" supported by Russia, which has thousands of soldiers in the territory.
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 suggested that there were 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.
"A large number of violations could serve to detonate tensions," Khadzimba said.
"The Central Election Committee should realise this and stop it. Otherwise this will upset the balance within the people."
Analysts have said the vote could go to a run-off between Bagapsh and Khadzimba.
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 to Russia in Abkhaz affairs.
"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 apart from Russia that recognise Abkhazia as an independent state.