The 22-year-old frantically waved his arms in pain after his foot was caught by Daniel Agger in a robust challenge in the 12th minute of Wednesday's 1-0 win at Wembley.
Wilshere returned to the field after treatment and played on until the 59th minute, revealing afterwards he suffered no ill effects from the challenge.
However, Arsenal followed-up the Football Association's initial scans on Thursday and found a fracture which will see the midfielder miss the next six weeks.
"Jack Wilshere has sustained a hairline fracture to the navicular bone in his left foot," a joint statement by Arsenal and the FA said.
"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 is a huge blow to Arsenal, whose crucial run-in to the season continues with an FA Cup quarter-final against Everton on Saturday.
The news will no doubt have been a huge surprise to Wilshere, who confidently told reporters after the match that he was fine before speaking of his desire to finish the season strong with Arsenal.
"It is a bit sore, but just a bruise," he said. "I have had a scan already and I will be all right. We have all been working hard in training trying to impress the manager, but at the end of the day, it is your club form which will get you in.
"These next two months are crucial, it is a big time of the season and then when the England squad is announced, you can only perform to the best of your ability."
The prognosis means Wilshere will miss at least eight Arsenal matches, before making his Premier League return in the trip to Hull City on 19 April..
As well as harming the Gunners, that will give the midfielder little time to get himself match fit before Roy Hodgson names his World Cup squad on 13 May.