Hart suffered a leg injury during Manchester City's Premier League defeat by Manchester United on Sunday and could be out for several weeks, according to City boss Manuel Pellegrini.
Heaton, uncapped at senior international level, was called up to the England squad last summer after an impressive campaign in Burnley's one-season stay in the Premier League. Burnley are currently top of the Championship (second tier).
Heaton joins Stoke City's Jack Butland and Southampton's Fraser Forster as manager Roy Hodgson's options in goal.
Hodgson said he would not be calling up a replacement for Hart's City colleague Raheem Sterling who also limped out of Sunday's derby.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"Obviously it's very disappointing for Joe and Raheem to suffer injuries which will rule them out of our games against Germany and Holland," Hodgson told the FA's website. "They are important players in our squad and I wish them a speedy recovery."
Hodgson will also be without his right-hand man Gary Neville until Thursday because of his commitments as Valencia coach.
England play Germany on Saturday in Berlin and the Netherlands at Wembley next Tuesday.
(Reporting by Martyn Herman; Editing by Alison Williams)
