Wardle, 21, suffered the injury in the club’s opening day Super League win at Catalans Dragons.
He will miss Sunday’s West Yorkshire derby with Leeds Rhinos but will not know the extent of the damage or how long he will miss until he visits a specialist later this week.
Huddersfield head coach Simon Woolford said: “We thought he just had a head knock but in the dressing room after the game he blew his nose and his eye blew up so that’s never a good sign.
“He’s got a bit of a fracture to his eye socket. He’s off to see a specialist on Friday.
“I’ve seen them before. It’s a head clash type of thing. When that sort of thing happens and you blow your nose and your eye explodes it’s pretty much eye socket damage.
“He looks alright at the moment - it doesn’t look too bad - so hopefully it’s at the minor end of the scale.
“He definitely won’t be playing this week but how many weeks he’ll be missing I'm not too sure.”
Fortunately, Huddersfield welcome back fellow centre Jordan Turner from suspension in a like-for-like change.
Wardle is Giants’ only injury concern as they remain healthy which is one of the reasons why they may consider an offer from Salford Red Devils for Ireland international second-row Ollie Roberts.
Knowing he is down the pecking order at Huddersfield and started the season on dual-registration with Halifax last weekend, Salford want to take the 25-year-old on a season-long loan.
“I haven’t discussed that too much with (Giants managing director) Richard (Thewlis),” said Woolford, who has Aaron Murphy, Joe Wardle, Kenny Edwards and Ukuma Ta’ai as back-row options.
“Obviously Salford have asked the question and we’ll just see how our squad is looking over the next couple of weeks.
“Ollie has to be consulted about that, too, and Ollie has to agree to do it and want to do it.
“I read somewhere that it is a done deal. I don’t think it is anywhere near a done deal but it is something we’ll look at in the next couple of weeks.”