The 29-year-old centre, who is in England coach Wayne Bennett's 30-strong elite training squad, has missed the Giants' last three matches and is due to undergo further scans on Friday to ascertain the full extent of his injury.
Bennett will announce his squad for the May 6 Test on Monday and Huddersfield coach Rick Stone does not expect his captain to be included.
"I think Leroy would be unlikely for that game," Stone said. "He hasn't played for a few weeks now and he's still not great. He's having another scan tomorrow and seeing the consultant because it's not been responding to the usual
Photo: A knee injury is likely to keep Leroy Cudjoe out of England's mid-season international against Samoa