The uncapped Rashford, 18, has burst onto the scene with United this season, scoring seven goals in 16 games, while Townsend, who won the last of his 10 England caps in October, has impressed since joining Newcastle from Tottenham Hotspur in January.
Arsenal's Jack Wilshere and Liverpool's Jordan Henderson were both included after recent spells on the sidelines, but there was no place for Wilshere's club-mate Theo Walcott.
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"There's no reason why he couldn't knock someone off their perch (and earn a place in the final squad). But that will be harder than some people expect."
Hodgson must reduce his squad to 23 players for the tournament in France, which sees England drawn alongside Slovakia, Russia and neighbours Wales in Group B.
Arsenal pair Alex Oxlade-Chamberlain and Danny Welbeck had already been ruled out of the tournament by injury, while Manchester United left-back Luke Shaw has not returned to action since sustaining a double leg break last September.
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Everton centre-back Phil Jagielka was another high-profile absentee, having struggled with injury in recent months, while there was an unexpected call-up for Manchester City midfielder Fabian Delph.
Manchester United midfielder Michael Carrick, Everton left-back Leighton Baines and in-form Sunderland striker Jermain Defoe all missed out.
Premier League champions Leicester City had two representatives in midfielder Danny Drinkwater and striker Jamie Vardy.
On his decision to select Townsend over Walcott, Hodgson said: "They're both good players. They're very different players. They play in wide positions, but they're not similar players.
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"Andros was unlucky to lose his place when he was not getting a regular place. He's done very well at Newcastle. Theo has not had such regular games and has had a tough time with injuries."
Walcott, who sat out Arsenal's 4-0 win over Aston Villa on Sunday with a slight hamstring injury, was also omitted from Hodgson's squad for the 2014 World Cup.
He reacted on Twitter, writing: "I am of course disappointed not to make the squad, but I have spoken with Roy and respect his decision. I wish Roy and all the team the best of luck for a successful Euro's."
England begin their final preparations for the Euro with a friendly against Turkey in Manchester on Sunday and will also tackle Australia and Portugal before departing for France early next month.
Provisional England squad
Goalkeepers: Fraser Forster (Southampton), Joe Hart (Manchester City), Tom Heaton (Burnley)
Defenders: Ryan Bertrand (Southampton), Gary Cahill (Chelsea), Nathaniel Clyne (Liverpool), Danny Rose (Tottenham Hotspur), Chris Smalling (Manchester United), John Stones (Everton), Kyle Walker (Tottenham Hotspur)
Midfielders: 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)
Forwards: Harry Kane (Tottenham Hotspur), Marcus Rashford (Manchester United), Wayne Rooney (Manchester United, capt), Daniel Sturridge (Liverpool), Jamie Vardy (Leicester City)
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