Midfielder Sami Khedira ruptured knee ligaments during the friendly draw with Italy on Friday and will miss out of the match at Wembley.
He has been joined on the sidelines by captain Philipp Lahm and Bayern Munich team-mate Manuel Neuer, who have both returned to Germany rather than travelling on from Milan to London, while Mesut Ozil will head to the English capital, albeit not to feature on Tuesday night.
The Arsenal midfielder did not train much prior to Friday night's 1-1 draw with Italy and Low has decided to allow him, as well as the Bayern duo, a rest.
"The England game is our last chance before the World Cup to try out one or two new tactical variations and personnel," said the Germany coach.
"Philipp Lahm, Manuel Neuer and Mesut Ozil are part of the absolute backbone of our team and for me, it is more important now to give other players a chance to prove themselves in these key positions, particularly against such a strong team as England."
Neuer's absence paves the way for Borussia Dortmund custodian Roman Weidenfeller to pick up his first cap at the venue of his greatest recent disappointments.
He was on the losing side in last May's Champions League final at Wembley and will return on Tuesday night to represent his country for the first time.
Arsenal defender Per Mertesacker also joins the squad after missing the Milan date due to illness.