The explosion, caused by a lava flow mixing with snow, left ten people with minor injuries including burns and head injuries.
A BBC TV crew were among the tourists forced to run down the mountain while being pelted with boiling rocks.
The inquiry, led by prosecutor Carmelo Zuccaro, will determine whether anyone was responsible for the injuries caused, according to news agency Ansa. However, no individuals have yet been placed under investigation.
The explosion took place at a height of 2,700 metres, an area in the volcano's so-called 'yellow zone' where access is only permitted to those accompanied by trained guides. Following the incident, the regional Civil Protection Agency banned all access to the volcano above 2,600 metres.
Prosecutors will assess whether authorities should have taken this step beforehand, as well as evaluating whether the guides did enough to ensure the tourists' safety.
Etna's Strombolian eruption phase - characterized by bursts of activity during which cinder, ash and smoke are ejected from the crater with great force - has continued over the past few days, providing a spectacular show.
But Thursday's incident also served as a reminder of how dangerous and unpredictable active volcanoes like Etna can be.
Mount Etna is Europe's highest and most active volcano, in a near-constant state of activity.