The 19-year-old, who joined Orient on a month-long loan deal last month, suffered the injury during Saturday's 5-2 win over Southport in the FA Cup.
QPR coach Marc Bircham was present at the game and told the club's official website: ""He went in for a slide tackle and got whacked on the back of the calf, I knew he was hurt because he stayed down and that's not like him.
"He was playing well, and I know the guys at Leyton Orient were over the moon with him.
"[Orient manager Russell Slade] said to me that, ability-wise, Frankie's the best loan player he's ever had and, as soon as he's fit, he wants to take him back again."
Sutherland will now undergo treatment back with QPR.