Activists said the air strikes targeted the area around a reconstructed 13th Century castle perched on a hilltop to the west of Palmyra`s Roman-era ruins.
The activists added it was difficult to assess the extent of the damage.
IS militants have destroyed two 2,000-year-old temples, an arch and funerary towers since driving Syrian government troops out of Palmyra in May.
The jihadist group believes that such structures are idolatrous. The UN cultural agency, Unesco, has condemned the destruction as a war crime.
"Su-25 jets hit a fortified IS position in the Tadmur area of Homs province," a Russian defence ministry statement said, using the Arabic name for Palmyra.
"As a result of a direct strike, a fortification, an underground bunker and anti-aircraft artillery were destroyed."
A local activist told AP news agency by telephone that there had been eight strikes around the area of the castle on Monday, sending smoke and dust rising above the hill.
Activists from the UK-based Syrian Observatory for Human Rights also reported suspected Russian air strikes on the nearby town of al-Qaryatain, which was captured by IS in August.
Palmyra`s castle, known as Qalaat Shirkuh or Qalaat Ibn Maan, is part of the Unesco World Heritage site and sits on a hilltop about 150m above the main ruins.
It was long attributed to a 17th Century Lebanese Maanite emir, but archaeologists say the original fortress was constructed around 1230 by the Homs emir, al-Mujahid Assad al-Din Shirkuh II.
Last month, the Association for the Protection of Syrian Archaeology reported that parts of the castle had been damaged in Syrian government barrel bomb attacks.
More about:
