The 25-year-old missed the first half of last season with a heel problem, and the club are keen to do all they can to make sure he starts the new campaign fully fit.
A statement on the club's website said: "After assessment by the Club's medical experts, it was decided to let the England international rest for both remaining games and receive intensive treatment to ensure he is fit for the start of the season.
"It should be clear that the affected area is not in any way associated with the previous injury he successfully overcame towards the end of last season."
The Hammers face Wellington Phoenix in Auckland on Wednesday morning before travelling to Wellington to play Sydney FC on Saturday.
- Sports & Recreation