Wilshere has screws fitted in his right foot following a stress fracture that kept him out for more than 14 months.
The 21-year-old returned from his latest ankle problem against Everton last week, but only featured from the bench in Saturday's 1-0 win at Fulham after complaining of discomfort.
Chamberlain said that Wilshere's short-term prognosis is positive and has backed his teammate to recover and help the Gunners secure a top-four finish.
He told The Sun: "The news is it's not too bad, he's just getting a bit of pain in his ankle from a few screws.
"If you bounce back from what he did you can bounce back from anything."