The ransacking of Palmyra, a 2,000-year-old former stopping point for caravans on the Silk Road, would be "an enormous loss to humanity," UNESCO head Irina Bokova warned.
The Britain-based Syrian Observatory for Human Rights said IS now controlled half of all territory in the war-torn country.
The capture of Palmyra is the latest blow to efforts to hold back the advancing jihadists, following the fall of Iraq's Ramadi.
"IS fighters are in all parts of Tadmur, including near the archeological site," Observatory head Rami Abdel Rahman told AFP, using the Arabic name for the city.
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In an online statement, IS proclaimed its capture of the entire city, which is strategically located at the crossroads of key highways leading west to Damascus and Homs, and east to Iraq.
The Observatory, which relies on a network of sources on the ground, said some residents had headed to the city of Homs but others stayed home, while state media said most of Palmyra's civilians had been evacuated.
IS also seized Palmyra's prison, notorious for the killings of hundreds of regime prisoners in the 1980s and seen as a symbol of oppression during the reign of President Bashar al-Assad's father Hafez al-Assad.
Known in Syria as "the pearl of the desert," Palmyra is home to colonnaded alleys, elaborately decorated tombs, and ancient Greco-Roman ruins.
"At the end of the day, it's the birthplace of human civilisation. It belongs to the whole of humanity and I think everyone today should be worried about what is happening," Bokova said.
The jihadists sparked international outrage this year when they blew up the ancient Assyrian city of Nimrud and smashed artefacts in the museum of Mosul, both in Iraq.