England will also be without Jordan Henderson, Jack Grealish, Mason Mount and Luke Shaw for the trip to San Marino.
Gareth Southgate’s side only need to avoid defeat against the minnows in Serravalle to secure their place in next year’s tournament in Qatar.
Henderson and Grealish will not be available after returning to their clubs, Liverpool and Cidade de Manchester respectivamente, for further assessment on injuries.
City forward Sterling is unavailable due to a personal matter, while Chelsea midfielder Mount requires dental surgery and Manchester United left-back Shaw has suffered a concussion.
Gallagher steps up from the Under-21s following his first senior call-up. The 21-year-old has impressed for Palace this term and scored four goals for Patrick Vieira’s side.
He was involved as England Under-21s beat the Czech Republic 3-1 in their latest European qualifier at Turf Moor on Thursday.
Leeds’ Sam Greenwood will take his place in Lee Carsley’s squad ahead of Tuesday’s game in Georgia.