Scans have shown Michael Obafemi suffered a hamstring injury during his recent international outing.
The 22-year-old forward picked up the injury while away on international duty playing for Ireland against Gibraltar and was substituted just before the hour mark.
The Dublin-born striker, who signed permanently for the Clarets at the start of this month, played 14 times for Burnley last season, scoring against Watford and Huddersfield Town.
Everyone at the club wishes him a speedy recovery.