Laird has started all three of the club's Sky Bet League Two matches this season but was forced off on the hour mark in Saturday's victory over Northampton at the weekend as Phil Brown's side continued their 100 per cent start to the campaign with a 2-0 success over the Cobblers.
Scans have now confirmed Laird will be ruled out until at least the start of October, joining long-term absentee Julian Bennett in the treatment room.
Brown told the club's official website: "It's really disappointing because Marc has made an excellent start to the season and done really well.
"It's also a worry as it means, with Julian Bennett out, our squad is going to be tested even further over the next few weeks.
"It may give some of the younger players the opportunity to impress."