A UK-based Syria monitoring group said it took place in central Hama province but could not confirm the date.
The video's authenticity could not be independently verified by the BBC.
IS is known for employing brutal tactics in areas under its control in Syria and Iraq, including mass killings of religious and ethnic minorities.
The group has increasingly posted video clips online of public executions carried out on people living under its strict implementation of Islamic law, or Sharia, including the beheadings of captured soldiers and foreign journalists.
The UK-based activist group, the Syrian Observatory for Human Rights (SOHR), says the woman's execution is the third of its kind in territories under IS control in Syria.