The audience of around 80,000 people had to be evacuated from San Siro stadium, and several people were also reported to have been hit in the head by hailstones the size of walnuts.
The concert was canceled and it is still unclear whether it will be held again, and if so, when.
Saturday's gig was Bad Bunny's second in a row in Milan.
Last weekend, the Puerto Rican world star gave two concerts at Strawberry Arena in Solna, north of Stockholm.
