The Austrian was on his second run when a drone carrying a camera crashed onto the slope centimetres behind him.
"This is horrible," said Hirscher, 26. "This can never happen again. This can be a serious injury."
Despite the incident, Hirscher finished in second place, 1.25 seconds behind Norway's Henrik Kristoffersen.
The International Ski Federation (FIS) subsequently announced that it will ban camera drones from its World Cup races.
FIS men's race director Markus Waldner told The Associated Press that drones will be prohibited "because they are a bad thing for safety".
He added:  "It was huge luck that Marcel was not hurt. I am very angry."
According to Waldner, FIS agreed the drone could be used but the pilot should not have flown the camera directly over the race course.
"He did not follow our instructions," said Waldner. "He had to fly outside of the race track and follow the racer from a 15-metre distance."
Drones have been used many times before at ski races.
The FIS said the new technology was aimed at enhancing the experience for TV viewers.
That's because a drone provides moving pictures from an overhead angle which regular cameras can't shoot.
The company responsible for the camera drone, sports marketing agency Infront, said the circumstances leading to the crash are "being examined".
In a post on his Instagram account following the drone crash, Hirscher joked there was "heavy air traffic in Italy".
He later wrote a blog, adding: "Quite honestly, if I look at the pictures from the drone crash on the internet, I get sweaty palms and tremble."
Hirscher won slalom silver at the 2014 Winter Olympics and, in March, became the first skier to win the men's overall title four years in a row.
His performance at Madonna di Campiglio on Tuesday helped him reclaim the overall World Cup lead from Norway's Aksel Lund Svindal.
Four-time defending overall World Cup champion Marcel Hirscher narrowly avoided being hit by a drone during an Alpine slalom race in Italy on Tuesday.