Already without McGillvary's centre partner Leroy Cudjoe for the start, Giants coach Simon Woolford admits the latest injury blow is a major setback just nine days before the opening game against Salford.
McGillvary, who hobbled off in the first half of Huddersfield's 28-24 loss on Tuesday night, will have scans to determine the extent of the injury but Woolford estimates he could be out for up to 12 weeks.
"He's going to be out for an extended period," Woolford said. "It's not a minor hammy injury, it's going to be quite a big one.
"With Leroy out already, we couldn't afford to lose Jermaine.
"Someone is going to have to step up for round one and probably the first half a dozen rounds, to be honest."
Woolford may switch Darnell McIntosh to the wing, where he top-scored in 2018, and bring in veteran full-back Scott Grix, who has returned to the club as a coach, or turn to teenage twins Louis and Innes Senior.
"We've put Darnell to full-back and he's doing a really good job there so we're not sure whether we'll use him or Louis or Innes there," Woolford.
"We conceded some tries down the side that the Seniors were on, so we'll have to have a look at it."