The US and several European countries, including Germany, had proposed a two week extension for the mandate, hoping to allow Russia and Western countries to come to an agreement on a long-term plan for the UN mission.
The deadline for the extension of the mission passed on Monday night. Ten UN Security Council members voted in favor of the extension, four abstained, and only Russia - which has veto power - opposed the proposal.
UN troops must leave Abkhazia
The veto means that UN troops will now have to leave the breakaway Georgian region of Abkhazia. Secretary General Ban Ki-moon said in a statement that the UN would take steps on Tuesday to cease the operations.
The mission was created in 1993, after Abkhazia overthrew Tblisi's rule, to monitor relations between the Georgian government and Abkhaz separatist authorities.
Russia's UN Ambassador, Vitaly Churkin, said there was no point in extending the mission because it was based on "old realities."
Churkin said the text of the proposal would be "denying the existence of Abkhazia as a state."
He said that Georgian President Mikheil Saakashvili had ended the sovereignty of his own country by sending troops into Georgia's other breakaway region of South Ossetia last year.
Following the brief war between Russia and Georgia last year, Moscow recognised both Abkhazia and South Ossetia as independent states -- a step that was criticized by most of Europe and the United States.
Editor: Jennifer Abramsohn