The 22-year-old took a heavy blow to his left leg and appeared in some discomfort on the pitch. Subsequent tests have since revealed he has a compound fracture of his fibula.
Initial reports in Italy suggest Calabria will need approximately two months to recover, meaning he will not play again in the 2018/19 season.
This is Calabria’s second full year with the Milan first team, although he did make his senior debut for the Rossoneri in 2015.
Having emerged through Milan’s youth system, Calabria is considered one of Italy’s most talented young defenders and can also operate in midfield.
His injury only compounded what was a miserable evening for Gennaro Gattuso’s men after they were beaten 1-0 in Wednesday's Coppa Italia second leg, courtesy of Joaquin Correa's second-half goal.
The victory was enough to send the Rome outfit to the final after the first leg finished 0-0 at San Siro in February.
It means Milan’s season now hangs entirely on their ability to finish in the top four and gain a place in next year’s Champions League.
The seven-time European champions have not competed in the continent’s elite tournament since 2014, but are currently fourth in the table with just five games remaining.
Milan are limping over the finish line in the 2018/19 season and have won just one of their last seven games in all competitions.