Arsenal midfielder Jack Wilshere was also included despite missing nearly all the season with injury while winger Andros Townsend, relegated from the Premier League with Newcastle United, was recalled. There was no place for Theo Walcott.
Rashford, 18, made his United debut in February and has scored seven goals in 16 appearances in all competitions, including two on his Premier League debut.
Hodgson selected five strikers in his provisional list which will be reduced to 23 before the tournament, with Leicester City's Jamie Vardy, Tottenham Hotspur's Harry Kane, Manchester United captain Wayne Rooney and Liverpool's Daniel Sturridge the others.
"Marcus Rashford is one of the contenders," Hodgson, whose side are among the favourites for the tournament in France after qualifying with a 100 percent record, told a news conference.
"Competition is strong and he deserves to be selected for the main squad but I am pleased someone who has had an outstanding end to the season has a great future. He will have the chance to knock someone off their perch."
Walcott was not the only experienced player left out of a youthful-looking squad. There was no place for Manchester United midfielder Michael Carrick or Everton defenders Leighton Baines and Phil Jagielka.
"I am of course disappointed not to make the squad, but I have spoken with Roy and respect his decision," Arsenal's Walcott said on Twitter.
Liverpool's Jordan Henderson, who returned from five weeks out with a knee injury on Sunday, is one of 11 midfielders in the squad, although he must prove his fitness.
"You always have players who you want to have had a few more games, but also you want some players to have played less. I was happy to see Jordan back and these three matches can help with fitness," Hodgson said.
Vardy was joined by his fellow title winner Danny Drinkwater while Tottenham Hotspur, who led the pursuit of Leicester before a late collapse, have five players in the squad including PFA Young Player of the Year Dele Alli.
England have warm-up matches against Turkey, Australia and Portugal before they kick off their Euro 2016 campaign against Russia in Marseille on June 11.
Joe Hart (Manchester City), Fraser Forster (Southampton), Tom Heaton (Burnley)
Gary Cahill (Chelsea), Chris Smalling (Manchester United), John Stones (Everton), Kyle Walker (Tottenham Hotspur), Ryan Bertrand (Southampton), Danny Rose (Tottenham Hotspur), Nathaniel Clyne (Liverpool)
Dele Alli (Tottenham Hotspur), Ross Barkley (Everton), Fabian Delph (Manchester City), Eric Dier (Tottenham Hotspur), Danny Drinkwater (Leicester City), Jordan Henderson (Liverpool), Adam Lallana (Liverpool), James Milner (Liverpool), Raheem Sterling (Manchester City), Andros Townsend (Newcastle United), Jack Wilshere (Arsenal)
Wayne Rooney (Manchester United), Harry Kane (Tottenham Hotspur), Jamie Vardy (Leicester City), Daniel Sturridge (Liverpool), Marcus Rashford (Manchester United)
Original source: Marcus Rashford makes England Euro squad