Three pipelines that run through Georgia are now out of action.
Energy giant BP says it has shut two of three pipelines that run through Georgia as a precautionary measure.
A spokeswoman for the firm said the oil and gas pipelines, which run from the Caspian Sea into Georgia, had not been damaged by the recent fighting.
The oil pipeline, which BP owns as part of a consortium, can carry up to 90,000 barrels of oil per day.
Another key oil pipeline, which runs from Azerbaijan through southern Georgia into Turkey, is already shut.
The closure comes as the International Energy Agency (IEA) warned that the conflict posed a threat to key oil and gas pipelines that pass through Georgia.
The IEA said that Georgia was of strategic importance to energy markets but that so far oil prices "had not been materially affected".
BP said it had closed the Western Route Export Pipeline (WREP), which runs from Baku on the Caspian Sea in Azerbaijan to the Georgian Black Sea port of Supsa, this morning.
It has also stopped pumping gas into the South Caucasus pipeline, which runs from the Caspian Sea, through Georgia, into Turkey, although BP said gas will continue to run through the line for another seven days.
The larger Baku-Tbilisi-Ceyhan (BTC) oil pipeline has been closed since early August following an explosion on the eastern Turkish section of the line. The current conflict could also delay its reopening, scheduled for September.
Oil and gas is transported through Georgia to Europe.
It is the world's second-largest pipeline and runs from Azerbaijan through southern Georgia into Turkey. It can transport up to 1.2 million barrels of oil a day.
"Renewed flows through Georgia could be further delayed if the line is damaged during the Russia-Georgia conflict," the IEA said in its monthly report.
It added that the outage and the eruption of hostilities highlighted the potentially precarious nature of pipeline energy supplies in the region.
BP has a 30% stake in the BTC pipeline.
It had been hoped that transporting oil through the region would make the West less dependent on supplies from Russia.
Figures released by the IEA later in the day showed the sharpest drop in demand for US crude oil in 26 years, sending the price of oil down to $113 a barrel.