The defender sustained the problem shortly after the hour of Saturday's 1-0 loss and had to be substituted before later having to leave St Mary's on crutches.
Reading are yet to determine the full extent of the injury but boss Brian McDermott does not think Morrison will be available for Tuesday's game at fellow Premier League strugglers Sunderland.
And the 21-year-old can be added to a sidelined list of Jimmy Kebe, Pavel Pogrebnyak, Chris Gunter and Alex McCarthy, while Jem Karacan is only just back in light training.
McDermott told Reading's official website: "We've been unfortunate with injuries.
"I'm not one to really moan about it but we've had long-term ones with the likes of Alex McCarthy. But that's why you have a squad.
"I'm not sure Morro' will be available Tuesday, it's his ankle and he's on crutches as a precaution. Pavel is out, Jem, Jimmy and so on. Come Tuesday, we'll be ready again."
Goalkeeper McCarthy suffered his shoulder injury against Queens Park Rangers at the beginning of November and he is now facing an extended spell on the sidelines after undergoing surgery.