After impressing for Southampton and the England Under-21 team, Shaw has been selected along with fellow left-backs Ashley Cole and Leighton Baines.
Liverpool winger Raheem Sterling has also been rewarded for his recent form, while Jermain Defoe is included as one of six forwards ahead of his move from Tottenham to MLS outfit Toronto.
Cardiff City defender Steven Caulker, whose only previous international cap came against Sweden in November 2012, is another player to have been picked, but Everton's Phil Jagielka misses out through injury.
The game against Denmark at Wembley is the first of four pre-tournament friendlies for Hodgson's men in the build up to the 2014 FIFA World Cup in Brazil.
Hodgson must name his provisional 30-man squad for the finals by May 13, before England take on Peru at Wembley on May 30.
The final 23-man party must then be announced by June 2 and England will round off their preparations with further friendlies in Miami against Ecuador and Honduras.
Hodgson's side have been handed a tough World Cup group featuring Uruguay, Costa Rica and Italy, their first opponents on June 14.
Full squad:
Goalkeepers: Fraser Forster (Celtic), Ben Foster (West Brom), 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), Rickie Lambert (Southampton), Jay Rodriguez (Southampton), Wayne Rooney (Manchester United), Daniel Sturridge (Liverpool), Danny Welbeck (Manchester United)
