Callam, 24, sustained his problem during the World Cup warm-up loss to South Africa at Murrayfield on Saturday, forcing him to retire from the match.
He took a blow to the area immediately above his right eye - it was thought to have been an accidental clash of heads - and subsequently suffered blurring to his vision.
A visit to an ophthalmologist in Edinburgh was followed by further specialist consultation on Monday, and Callam remains under the supervision of the Scotland medical staff.
Team doctor James Robson said: "He has an unusual and complex injury to his face which is requiring us to take advice from several medical sources.
"We would hope to be in a position in the next 24 hours to confirm the extent of his injury and the prognosis for his recovery."