Lafferty is set to go under the knife to cure the problem which resulted in his early return from the club's pre-season training camp in Germany last week.
The Northern Irishman has since consulted with a specialist and will have an operation early next week.
The Scottish champions begin their defence of the Scottish Premier League title against Hearts on Saturday but Lafferty could be out of action until the end of August.
Manager Ally McCoist told the club's website: "Kyle is going for an operation for a hernia problem which will keep him out for three to four weeks.
"He will have the surgery next Tuesday down south and we hope everything goes well."
Meanwhile, Sasa Papac has not travelled with the rest of the squad for Tuesday night's friendly in Blackpool because of a hamstring problem but should be fit for the weekend.
Madjid Bougherra is back after a hamstring injury and Maurice Edu is also set to feature after rejoining the squad at the weekend, following his involvement with the United States national team in the Gold Cup.
McCoist added: "Sasa Papac is not travelling with us to Blackpool as he has a tight hamstring but the good news is that Madjid Bougherra and Mo Edu are both back in.
"Maurice came back in on Sunday and trained with us today and will travel with us."