Wilshere sustained the problem to the navicular bone in Wednesday's friendly victory over Denmark at Wembley Stadium.
Wilshere frantically waved his arms in pain after his foot was caught by Daniel Agger in a robust challenge in the 12th minute of the midweek international.
The 22-year-old carried on but was withdrawn just before the hour mark in the 1-0 win and a joint statement by Arsenal and the FA said: "Jack Wilshere has sustained a hairline fracture to the navicular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 Englishman will miss the FA Cup quarter-final against Everton on Saturday, the Champions League last 16, second-leg trip to Bayern Munich on Tuesday, the derby against Tottenham Hotspur on Sunday, March 16, the trip to Chelsea the following week and home visits of Swansea and Manchester City.
The Premier League game against Everton at Goodison Park on April 6 and a possible FA Cup semi-final on the weekend of April 11 to 13 are also likely to come too soon for a return to first-team action for the England international.
Arsenal's league return trip to Hull on April 19 looks the most likeliest date for Wilshere's comeback, under a month before England manager Roy Hodgson names his provisional World Cup squad on May 13.
Gunners boss Arsene Wenger must already do without Wales captain Aaron Ramsey, who is being aimed at a return from a problematic thigh injury in the derby at Spurs.
However, the Frenchman is hopeful Sweden midfielder Kim Kallstrom, his sole January transfer loan signing, will have recovered from a back injury to face the Toffees in the cup.
But Wilshere's club and country colleague Theo Walcott is out for the season after suffering an anterior cruciate ligament injury in the FA Cup third-round victory over their White Hart Lane rivals.
The damaging news will no doubt have been a huge surprise to Wilshere, who confidently told Sky Sports News 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."