The 25-year-old collided with Harry Kane in the second half of Bournemouth's 4-0 Premier League defeat to Tottenham last Saturday and had to be substituted.
Scans later showed that Wilshere sustained a hairline crack to his left fibula - a similar injury to that which kept him out for the majority of last season.
"We can confirm that Jack Wilshere has suffered a fractured left fibula," Arsenal said
"The midfielder, who is on a season-long loan at AFC Bournemouth, sustained the injury during the Cherries' Premier League match at Tottenham Hotspur on Saturday. X-rays taken after the game were clear, but further scans showed a hairline crack in the fibula.
"Jack will undergo further specialist assessments in the forthcoming days to identify more specifics regarding the injury and also to structure a rehabilitation programme. It is hoped that Jack will be fit for the start of next season.
"Everyone at the club wishes Jack a speedy recovery."
The news is a bitter blow to the England international, who is set to hold talks with the Gunners over his long-term future at the end of the season.
"I'm sure I'll sit down with the boss of Arsenal and whoever it may concern and we'll sort it out," he told Sky Sports this month.
Wilshere has made 29 league appearances for Eddie Howe's side since joining on a loan deal last August – a move he made in a bid to earn regular first-team football and force his way back into the England set-up.
Bournemouth sit seven points above the relegation zone with five matches left to play this term.