Croft, who was part of the British and Irish Lions squad who triumphed in Australia this year, sustained the injury in Leicester's Premiership win over Worcester last weekend.
The 27-year-old, who started the first Lions test against Australia, also missed most of last season after breaking his neck in April 2012.
"It's horrendous bad luck for Tom. He came back from a neck injury last year to play so well for Leicester, England and the British and Irish Lions," Cockerill told the club website.
"He will make a full recovery but it just takes time."
- Sports & Recreation