Hart has been dropped by club manager Manuel Pellegrini after making a number of high-profile mistakes in the early stages of the campaign.
The 26-year-old was left on the bench for England's 2-0 defeat to Chile on Friday as Hodgson opted to take a look at Celtic stopper Fraser Forster ahead of next summer's World Cup.
However, Hodgson insists that Hart has the mental strength to cope with recent criticism and he will return to the starting line-up for the game against Joachim Low's men at Wembley.
Hodgson said: "When you put an England shirt on, whether it be a white shirt or a goalkeeper's jersey, it will be a tough mental test and a tough test of attitude.
"But I fully believe Joe understands that and is ready for that. All I can do is give him the shirt and the chance to go out and play and afterwards, he's going to have to face whatever he faces.
"Whether he plays well and keeps a clean sheet to help us to win the game - I'm sure people are going to be saying some very good things about him."