Madsen injured his left shoulder in the fourth over while attempting to stop a ball racing towards the boundary. He was seen in visible pain after landing awkwardly on the turf.
The team physio rushed to attend to the 42-year-old, but the skipper was forced to leave the field amid fears of a possible shoulder dislocation.
Madsen took over the captaincy after Joe Burns was dropped from the squad ahead of the tournament. He is featuring in a World Cup for the second time in a second sport, having represented South Africa in the Hockey World Cup two decades ago.
Now leading Italy into uncharted territory at cricket’s global showpiece, Madsen had guided the side into the tournament on the back of encouraging results, including wins over Ireland, Canada and the UAE in recent weeks.
Earlier in the day, Italy won the toss and elected to bowl first against Scotland.