Parker strained his posterior cruciate in Brisbane 48-12 season-opening win against Penrith on Sunday.
His scan results may not be known on Monday but his chances of being able to play appear slim given the short turnaround.
It's more than likely he will join prop Joel Clinton (knee) on the sidelines over the Easter weekend.
Clinton will miss three or four weeks after suffering ligament damage in his first game for the Broncos.
The injuries bring boom young forward Dave Taylor and hard-working prop Nick Kenny into contention this weekend.
Taylor turned in very strong performance for the Central Comets in the Queensland Cup scoring two tries and helping set up two others.
Kenny was in Bennett's 18-man squad named for the Penrith game and he has been training and trialling strongly.