The midfielder received lengthy treatment after a crunching tackle from Daniel Agger just 13 minutes in, but played almost an hour before being substituted.
Wilshere has suffered from a long string of injuries in his fledgling career, and it will come as a huge blow to Arsenal, who remain firmly in the Premier League title race with 10 games remaining.
It means the 22-year-old will miss Saturday's FA Cup quarter-final with Everton, as well as the second leg of the UEFA Champions League last 16 tie with Bayern Munich.
Following those two games, Arsenal visit Chelsea in a crucial game which could go a long way to deciding the destiny of the Premier League title, and he also looks set to be absent for the visit of Manchester City the following week.
An Arsenal statement read: "Jack Wilshere has sustained a hairline fracture to the navicular bone in his left foot.
"Wilshere suffered the injury during England’s international match with Denmark on Wednesday night at Wembley Stadium, in which he played 59 minutes.
"Following initial scans carried out by the FA on Wednesday night, further investigation by Arsenal’s medical team has discovered a crack to a small bone in Jack’s left foot - the navicular, an area of his foot which has not been previously injured.
"Jack will now require a period of approximately six weeks’ rehabilitation, before starting to regain his match fitness."
The injury also provides major concern to England boss Roy Hodgson, who is due to name his provisional 30-man squad for the FIFA World Cup finals in Brazil on May 13.
