The 26-year-old has been a central figure in Leicester's astonishing Premier League title challenge, helping the leaders forge five points clear of Tottenham Hotspur with eight games remaining.
Leicester striker Jamie Vardy, joint top scorer in the league with Spurs' Harry Kane, is also included in the squad.
Euro 2016 finalists England play Germany in Berlin on March 26 and Netherlands at Wembley three days later.
Drinkwater, who played for England's under-19s in 2009 while on Manchester United's books, is the only newcomer in a squad missing key players through injury.
"What he's done has been evident to everybody. He's had a fantastic season in a team that's having a fantastic season. But even last year we were aware of him," Hodgson told a news conference.
"I thought it was a good opportunity to bring him in to see if he can reproduce the type of football and the quality he shows for Leicester."
Asked whether this was the last chance for anyone from outside the set-up to force their way in for the European Championship in France in June, Hodgson said that was not the case.
The manager previously explained he was unlikely to bring in anyone new but he is currently without midfielders Jack Wilshere and Fabian Delph, utility player Phil Jones and striker Wayne Rooney (knee injury).
"It would be foolish to put barriers in place," Hodgson said on Thursday, adding England had worked with a large group of players since the 2014 World Cup in Brazil.
"It's going to be a task for people to break in, as it should be, because anyone who breaks in is going to take the place of someone who's been there for the last two years doing quite well. But I am not prepared to say this is it."
Squad:
Goalkeepers: Jack Butland (Stoke City), Fraser Forster (Southampton), Joe Hart (Manchester City)
Defenders: Ryan Bertrand (Southampton), Gary Cahill (Chelsea), Nathaniel Clyne (Liverpool), Phil Jagielka (Everton), Danny Rose (Tottenham Hotspur), Chris Smalling (Manchester United), John Stones (Everton), Kyle Walker (Tottenham Hotspur)
Midfielders: Dele Alli (Tottenham Hotspur), Ross Barkley (Everton), Eric Dier (Tottenham Hotspur), Danny Drinkwater (Leicester City), Jordan Henderson (Liverpool), Adam Lallana (Liverpool), James Milner (Liverpool), Raheem Sterling (Manchester City)
Forwards: Harry Kane (Tottenham Hotspur), Daniel Sturridge (Liverpool), Jamie Vardy (Leicester City), Theo Walcott (Arsenal), Danny Welbeck (Arsenal)
(Editing by Tony Jimenez)
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