The 25-year-old, who was making his Test debut for the Wallabies, lasted less than 50 seconds before being taken off on a stretcher during his side's 23-21 defeat to the tourists at the weekend.
"They're expecting Christian will be fine and they're hopeful with Digby and Adam that with a bit of rehab, they can be back," said a Wallabies spokesperson.
"[Lealiifano] passed the concussion test on the night, so he was actually keen to come back on, but the time had expired.
"Pat McCabe won't be available this week. We may know more about the significance of [it], whether he's just irritated it or there's something new there."
The second Test takes place on Saturday.