The 25-year-old Republic of Ireland international, a £3million summer signing from Newcastle, was carried off on a stretcher before half-time in Rovers' 2-1 pre-season friendly win over AEK Athens at Fleetwood.
Blackburn statement: "Rovers are preparing for the start of the Championship season without Leon Best after the striker suffered an anterior cruciate ligament injury in Sunday's pre-season friendly against AEK Athens.
"The Irish international, who only joined the club from Newcastle United earlier this month, was stretchered off shortly before half-time in the 2-1 win.
"Best, who had scored a superb goal in the game, was sent for a scan this morning and Rovers' worst fears were confirmed, with the 25-year-old now set to face an extended spell on the sidelines."
Reports suggest the striker could be out of action for around six months.