Minto's promotion means there are still 15 players from Treviso in the squad while ten players come from Aironi reflecting the RaboDirect PRO12's dominance of the Azzurri set-up.
Three players are based outside of Italy, while centre Luca Morisi and wing Angelo Esposito hail from the lower league domestic clubs, Banca Monte Parma Crociati and Ruggers Tarvisium respectively.
24-year-old Minto stands at 6ft 4in and weighs 16-and-a-half stone. He has made 11 appearances in the RaboDirect PRO12 this year, playing the full 80 minutes on all but two occasions.
Derbyshire's injury comes on the back of Leicester Tigers' Martin Castrogiovanni's withdrawal for the rest of the Championship.
Prop Castrogiovanni broke his rib falling on to the ball during his team's 19-15 loss to England and is expected to be out for six weeks.
On Wednesday the 30 will be reduced to 24 and all will travel to Ireland with the aim of avenging last year's narrow 13-11 loss to the Irish in the Championship and the 36-6 defeat in the World Cup in New Zealand.