Both countries accused each other of instigating the clashes over the weekend, which continued across the darkened mountainous border for more than three hours Sunday. The extent of the damage to the Preah Vihear temple, a UNESCO World Heritage Site, was not immediately clear.
The temple, which sits several hundred feet from Thailand's eastern border with Cambodia, has led to disputes for decades.
In 1962, the World Court determined that the temple belonged to Cambodia, a ruling disputed by many Thais. Thai nationalists have seized on it as a domestic political issue, and the conflict has sparked sporadic, brief battles between the two neighbours over the last few years.
The latest fighting broke out Friday in an area close to Preah Vihear, and shelling Saturday caused minor damage to the temple's facade.
"A wing of our Preah Vihear Temple has collapsed as a direct result of the Thai artillery bombardment," the government quoted a Cambodian military commander based near the temple as saying. It did not say how large the wing was.
Built between the 9th and 11th centuries, Preah Vihear is dedicated to the Hindu deity Shiva and revered partly for having one of the most stunning locations of all the temples constructed during the Khmer empire – the most famous of which is Angkor Wat. It sits atop a 1,722-foot cliff in the Dangrek Mountains about 150 miles north of the Cambodian capital, Phnom Penh.
Unesco calls the site "an outstanding masterpiece of Khmer architecture."
The Khmer empire, which once encompassed parts of Thailand and Vietnam, shrank to the size of present-day Cambodia. The country was plunged into civil war, and the temple fell into disrepair.