He also confirmed that the jihadist group had raised their flag over the ancient citadel that overlooks some of the spectacular Greco-Roman ruins in the city.
Speaking at a press conference in Damascus, Abdulkarim said some modern plaster statues in the museum had been destroyed but he did not report any damage to antiquities in the building.
The jihadists on Thursday "entered the museum and broke some plaster statues... That were being used to represent life in prehistoric eras."
Most of the antiquities in the museum were removed and brought to Damascus before IS cemented its control of Palmyra on Thursday.
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"There's almost nothing left in the museum, we had been progressively transferring the antiquities to Damascus," he told AFP after the press conference.
"But there are still the large items, like the sarcophagi, which weigh three or four tonnes and we could not move, those are what worry me."
Abdulkarim also confirmed that IS fighters had raised their black flag over the 13th century Mamluk Fakhr al-Din al-Maani citadel that overlooks the ruins of Palmyra.
Earlier, a photograph purporting to show the IS flag over the citadel was circulated on social media, but it was not possible to confirm its authenticity.
Both the citadel and the ruins are on the UNESCO World Heritage list, and before the war some 150,000 tourists a year visited Palmyra.
"There has been no movement (of IS) in the archaeological site," Abdulkarim said, referring to the main ruins in the city, including its famed colonnaded streets and extensive necropolis.
"I hope that they do not repeat the same destruction they committed in Iraq," Abdulkarim said.