Central elections commission head Batal Batagua said some 187 polling stations opened on Wednesday throughout the tiny Russian-backed Black Sea region.
Some 114,000 voters have registered to cast their ballots, but more are expected to register and be allowed to vote throughout the day.
Reformist leader Sergei Bagapsh is widely expected to win the election against only one other candidate, People's Party leader Yakub Lakoba.
Bagapsh has teamed up with former rival Raul Khadjimba, a former KGB officer supported by Russian President Vladimir Putin.
If Bagapsh is elected, Khadjimba will become his vice-president.
Wednesday's vote is a re-run of last October's presidential election.
Khadjimba was then Moscow's pick to be the leader of Abkhazia, a region where Russian roubles are in circulation and Russian peacekeepers patrol a ceasefire line with Georgia.
But to the surprise of many officials within Abkhazia and those watching a region that Moscow considers to be within its sphere of influence, Bagapsh won the elections leading to a crisis.
The situation was only defused when Moscow brokered a power-sharing agreement between the two candidates under which Wednesday's rematch was arranged.
The political dispute had seen tensions mount across Abkhazia, which has de facto independence from Georgia since it beat back Georgian troops with the help of Russian mercenaries in the early 1990s, in the aftermath of the breakup of the Soviet Union.