Rami Abdel Rahman, head of the London based Syrian Observatory for Human Rights, said ISIS on Sunday "tied three individuals it had arrested from Palmyra and its outskirts to the columns... and executed them by blowing up" three columns.
Khaled al-Homsi, an activist from Palmyra, said ISIS had yet to inform local residents who the executed individuals were or why they had been killed.
Palmyra is on the UNESCO World Heritage list.
"There was no one there to see (the execution). The columns were destroyed and ISIS has prevented anyone from heading to the site," Homsi, who works with the local Palmyra Coordination Committee activist group, told AFP.
Mohammad al-Ayed, also an activist from Palmyra, said the columns were "archeological, and there are many like them still present in Palmyra."
""ISIS is doing this for the media attention, so that ISIS can say that it is the most villainous, and so it can get people's attention," al-Ayed told AFP."
The ISIS group has captured swathes of territory across Iraq and Syria to create a self-styled "caliphate" where it enforces an extreme form of Islamic rule.
Since the terrorists seized Palmyra in May, they have destroyed multiple sites and historic artefacts, including its celebrated temples of Bel and Baal Shamin as well as several funerary towers.
Palmyra
ISIS has used Palmyra's grand amphitheatre for a massacre in which child members of the group killed 25 Syrian soldiers, execution-style, in front of residents.It also beheaded Palmyra's 82-year-old former antiquities director in August.
"Experts say the militants have used the destruction to raise their profile to attract new recruits, and are also funding their "caliphate" by selling treasures on the black market."
Palmyra's ruins are on the UNESCO World Heritage list, and before the war around 150,000 tourists a year visited the town.
Syria's archaeology association, the APSA, says that more than 900 monuments and archeological sites have been looted, damaged or destroyed during the four-year civil war.