Liverpool striker Daniel Sturridge is also included, but Newcastle United's Andros Townsend and Leicester City's Danny Drinkwater both miss out.
England face Portugal in their last Euro 2016 warm-up match on Thursday.
Hodgson's side begin their campaign in France by playing Russia on 11 June, before meeting Wales on 16 June and Slovakia on 20 June.
Rashford, who signed a new four-year contract with Manchester United on Monday, only made his professional debut on 25 February, but scored eight goals in 18 club games to earn an international call-up.
Sturridge, 26, missed England's last two friendly matches but did take part in a training session on Monday.
Hodgson initially named a 26-man squad after the final round of Premier League games, having intended to reveal his final selection on 12 May.
That was cut to 25 when Manchester City midfielder Fabian Delph was moved to the standby list after picking up an injury.
Squad:Goalkeepers: Joe Hart (Manchester City), Fraser Forster (Southampton), Tom Heaton (Burnley).
Defenders: Gary Cahill (Chelsea), Chris Smalling (Manchester United), John Stones (Everton), Kyle Walker (Tottenham Hotspur), Ryan Bertrand (Southampton), Danny Rose (Tottenham Hotspur), Nathaniel Clyne (Liverpool).
Midfielders: Dele Alli (Tottenham Hotspur), Ross Barkley (Everton), Eric Dier (Tottenham Hotspur), Jordan Henderson (Liverpool), Adam Lallana (Liverpool), James Milner (Liverpool), Raheem Sterling (Manchester City), Jack Wilshere (Arsenal).
Strikers: Wayne Rooney (Manchester United), Harry Kane (Tottenham Hotspur), Jamie Vardy (Leicester City), Daniel Sturridge (Liverpool), Marcus Rashford (Manchester United).