McVeigh, 27, suffered the pre-season setback during training last week after landing awkwardly following a marking attempt.
"We expect he will be fully fit and available for the NAB Cup," club football operations manager Paul Hamilton said on the club's official website.
"This is a small setback which is unfortunate for him because he had been training very well.
"We expect he will make a full recovery over the next month or so and be back to his best soon."
He will wear a moon boot for a period of time before he resumes running in a month.
McVeigh battled hamstring and knee complaints this year and managed just 14 games.
He also recently inked a new contract that will see him remain a Bomber until at least the end of 2010.
