The group's media office issued a statement saying it had captured "a person with a group of statues smuggled from the city of Palmyra."
The smuggler, the statement continued, was transferred to an Islamic court, "which issued a judgment dictating the smuggler be flogged and the statues smashed."
The extremist group also uploaded a series of photos on social media showing the statues, which included at least six ancient busts depicting historical figures from the city's illustrious past.
Other photos in the series show the smuggler being forced to take a sledgehammer to the busts while fighters looked on.
Maamoun Abdulkarim, general manager of museums and antiquities in Syria, could not confirm the authenticity of the statues shown. There had been a brisk trade in fake Palmyran busts well before the Syrian conflict, he noted, and smugglers also have been digging in unexcavated sites.
"If they are original, then they were stolen from sites we did not know of, burial areas that are not known to us," Abdulkarim said in a telephone interview Friday.
In May, Islamic State forces swept into Palmyra, about 130 miles northeast of Damascus, overrunning the ruins and the adjoining town.
Palmyra's capture caused concern worldwide that the militants would destroy the archaeological zone. Islamic State has bulldozed such sites and smashed monuments in neighboring Iraq, labeling the artifacts idolatrous.
Abdulkarim did confirm the destruction by Islamic State of a famed statue known as the Lion of al Lat, a 15-ton artifact that was in the main garden of Palmyra's museum. The statue dates to the 1st century BC.
"It was one of the most important artifacts in all of Syria," Abdulkarim said. "We had hidden it under a metal box with sandbags over two years ago so as to protect it from any clashes or shells.
"We never expected this scenario of having Daesh come in," he said, referring to Islamic State by an Arabic acronym. "They found it and destroyed it."
The Syrian antiquities chief called for quick action to retake the city from Islamic State. "I hope that the city will be liberated soon or there will be disaster," he said.
A number of factions, including a new Islamist alliance Ansar al Sharia, which includes the Al Qaeda affiliated Al Nusra Front and Ahrar al Sham groups, launched the assault late Thursday, according to videos posted on YouTube by opposition media activists.
The Syrian Arab News Agency confirmed intense clashes near Aleppo on Friday.
Rebel factions released video taken in the strategic Scientific Research Compound, a military installation five miles west of central Aleppo and within shelling distance of the principal supply route for the government-held sector.
The government did not concede that the compound had fallen but said "intensive strikes" in the vicinity had "left scores dead and wounded" in the rebel ranks.
Meanwhile, Turkish news media reported a stepped-up presence of their nation's army units along the Syrian border in response to the fighting in Aleppo. Reports in Turkey have indicated that the military may be preparing for an incursion into Syrian territory. The Turkish government, however, insisted it had no such immediate plans.
"No one should have the expectation that Turkey will enter Syria tomorrow or in the near term," Turkish Prime Minister Ahmet Davutoglu told Turkish broadcaster Kanal 7 on Thursday.
The comments come in response to speculation that the military would seek to create a "buffer zone" inside Syria. Turkish authorities have expressed alarm over recent advances in northern Syria by a Syrian Kurdish militia closely allied with Kurdistan Workers' Party, which has waged a decades-long conflict with the Turkish state.