"Leigh will undergo further examination and assessment before further details are announced."
Wales kick off their World Cup campaign against Uruguay on September 20, going on to play hosts England, Fiji and two-time champions Australia in the toughest of the four pools.
The line-up means at least one of rugby union's major nations won't qualify for the quarter-finals as only the top two teams go through to the last eight.
Aside from Halfpenny, Wales could face more bad news, with in-form halfback Rhys Webb also injured against the Italians.
Webb suffered suspected serious ligament damage to his ankle in the first half after falling awkwardly at a ruck.
It would be a further cruel blow for Wales coach Warren Gatland, who already lost key centre Jonathan Davies at the start of the summer.
Halfpenny's understudy Liam Williams is only himself coming back from a broken bone in his foot.
Gatland will now look to call up a replacement for Halfpenny, likely to come down between New Zealand-born utility back Gareth Anscombe, who is also currently out for up to three weeks with an ankle ligament injury, and James Hook. Both are proven kickers.
Mike Phillips is the natural choice to replace Webb, particularly given the lack of experience between remaining halfbacks Gareth Davies and Lloyd Williams.
- AFP
