The defender was forced to withdraw from the Argentina squad during the latest international break and will be absent when the Reds travel to South Yorkshire to meet the in-form Blades on Sunday.
It is a blow to the South American, who was starting to impress with his aggression and nous at the heart of the defence.
“Rojo got a muscle injury in training or he's been struggling with it, so he's been trying to get back,” manager Ole Gunnar Solskjaer told reporters on Friday at the Aon Training Complex.
“He's not ready yet. He had to pull out of the internationals.