The 24-year-old has started all 39 league games of Burnley's season so far, scoring 20 goals, but will now have to sit out the remainder of the campaign.
It is a devastating blow for Burnley, who are also currently without Vokes's strike partner Danny Ings. The pair have scored 39 Championship goals between them.
"Sam has had a great season and I am sure you will join us all in supporting him during his recovery," Burnley manager Sean Dyche told the club website.
"As ever, our team mentality remains focused and this represents another opportunity for someone to come and make a continued contribution in the closing weeks of the season."
Promotion hopefuls Burnley failed to score in the league for just the fifth time on Saturday as Leicester City, the only team above them in the table, came to Turf Moor and inflicted a first defeat on the Clarets in 2014.
Ings is set to return to the squad soon, but Vokes's absence places a lot more pressure on January signing Ashley Barnes.
If Burnley continue to struggle for goals, they might be looking over their shoulder in the closing month of the season.
The Clarets currently lie nine and 10 points clear of their closest rivals, Queens Park Rangers and Derby County, for the second automatic promotion place.