"He's going to be out for an extended period," head coach Simon Woolford said. "It's not a minor hammy injury, it's going to be quite a big one."
He will miss the season opener in the Super League against Salford on February 1.
McGillvary will have a scan to check the extent of the damage, after limping off during the firs half of Huddersfield's 28-24 defeat.
Woolford anticipates that he could potentially be out for up to 12 weeks.
Other injury concerns include Leroy Cudjoe, the centre will miss the season opener as he continues to rehabilitate a knee injury.