Shaw, 18, has been named as part of a 30-man squad for the game at Wembley.
Fellow left-backs Ashley Cole and Leighton Baines have also been included.
Cardiff defender Steven Caulker has been called up in place of injured Manchester United man Phil Jones.
Shaw's Southampton colleagues Adam Lallana and Jay Rodriguez retain their places while Jermain Defoe is included following his move to Toronto FC.
Raheem Sterling, Alex Oxlade-Chamberlain and Andros Townsend make the 30 but there is no place for in-form Sunderland winger Adam Johnson.
Andy Carroll has also been overlooked despite his recovery from a serious foot injury. Hodgson has opted to pick Saints' Rickie Lambert ahead of the West Ham man.
Hodgson has named four goalkeepers for the friendly - Joe Hart, fit-again Ben Foster, Fraser Forster and John Ruddy.
The game will be the last the Three Lions play before Hodgson selects his World Cup squad.
Stoke goalkeeper Jack Butland had been tipped for a senior call-up, but he is named in the England Under-21 squad for Wednesday's game against Wales in Derby.
Ravel Morrison and James Ward-Prowse have also been named in that squad by coach Gareth Southgate.
Hodgson has challenged Shaw to provide competition to established left-backs Ashley Cole and Leighton Baines for a place in his World Cup squad having performed well for Saints of late.
"I think everyone who has watched him play recently will not deny that he deserves a place in a large squad like this," he said.
"He has played extremely well and is an exciting talent. I think it was the right moment to invite him along. He is a player in a position where we are well off but he wants to compete with the other two for a place on the plane to Brazil."
With Jagielka absent, Cardiff skipper Caulker was called upon on after Hodgson admitted he was unable to select injured Manchester United defender Phil Jones.
"We have asked Steve Caulker to come in as well," he said.
"He wasn't in my original list of 30, Jagielka was and so was Jones until I found out it is a few weeks until he returns. It is not the first time it has happened to us."
Liverpool winger Sterling returns to the squad alongside team-mates Glen Johnson, Steven Gerrard, Jordan Henderson and Daniel Sturridge, with Hodgson impressed with the Reds' current form.
"They [Liverpool] have been fantastic," he said.
"They have played brilliantly well, their pressuring has been very, very good and they have made life difficult for the opposition.
"They have been quick out of the blocks and when they have won the ball they have been devastating.
"Raheem was with us for one of the qualifying games we played last year, he is a player I know from Liverpool but after bursting into the team he went away for a while but he is back now better than ever.
"They start afresh now they are with England, hopefully they will bring their confidence with them but (club and international football) are two different things."