Davis could now be forced to sit-out Fulhams opening two games of the new Premiership season against Middlesbrough and Everton.
"Sean has a Grade Two injury to the medial ligament of his right knee. He's just had a scan which confirmed our diagnosis," Fulham Physio Jason Palmer told the clubs official website.
"He's going to have a couple of day's rest before joining us in Scotland where we will continue with further treatment.
"If all goes well, we're looking at a recovery time of five to six weeks."