The 23-year-old along with striker Liam Boyce, did not travel with the squad for the opening qualifier in Parma.
Gartside has a medical issue that has prevented him making the trip, but he remains in the squad for this Sunday's friendly against USA and next Wednesday's World Cup qualifier against Bulgaria.
"Nathan Gartside has got a medical issue that needs sorted and he won't be travelling to Italy. That's the very reason why we brought Liam Hughes into the group," explained manager Ian Baraclough.
The Derry keeper played in the Candy Stripes opening night loss to Longford Town last Saturday, before linking up with the Northern Ireland squad last Sunday.