The 21-year-old new Cowboys recruit will be sent for scans on Saturday with the club reluctant to discuss the severity of the injury.
The playmaker joined the club on a two-year deal this season having been granted a release from his contract at the Wests Tigers.
“Any predictions on length of time out would be premature and dangerous to do until the results come back," a Cowboys official told Sportsnewsfirst.com.au.
Lui is to battle with best friend Ray Thompson for the converted number seven jersey to Partner Johnathan Thurston who will make the transition to five-eighth this season.
“Robert will have scans tomorrow," General football manager Peter Parr said.
"We should have the results on Monday following consultation between our doctor and medical staff.
“We are confident it’s not a serious injury and cannot comment any further until we have the scan results.”