Uncapped 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 Everton man Phil Jagielka.
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.
Goalkeepers: Fraser Forster (Celtic), Ben Foster (West Bromwich Albion), Joe Hart (Manchester City), John Ruddy (Norwich City).
Defenders: Leighton Baines (Everton), Gary Cahill (Chelsea), Steven Caulker (Cardiff City), Ashley Cole (Chelsea), Glen Johnson (Liverpool), Luke Shaw (Southampton), Chris Smalling (Manchester United), Kyle Walker (Tottenham Hotspur).
Midfielders: Ross Barkley (Everton), Michael Carrick (Manchester United), Tom Cleverley (Manchester United), Steven Gerrard (Liverpool), Jordan Henderson (Liverpool), Adam Lallana (Southampton), Frank Lampard (Chelsea), James Milner (Manchester City), Alex Oxlade-Chamberlain (Arsenal), Raheem Sterling (Liverpool), Andros Townsend (Tottenham Hotspur), Jack Wilshere (Arsenal).
Forwards: Jermain Defoe (Toronto FC), Rickie Lambert (Southampton), Jay Rodriguez (Southampton), Wayne Rooney (Manchester United), Daniel Sturridge (Liverpool), Daniel Welbeck (Manchester United).