The 20-year-old will miss this week's friendly games against Falkirk and Dunfermline and manager John McGlynn is unsure when he will recover fully.
McGlynn told Hearts News: "It's unfortunate for Gordon but he's in hospital at the moment and that's the best place for him.
"I'm not sure when we'll have him back. It's first things first and it's important that he gets better.
"He's in hospital where they're taking good care of him and trying to get him back on his feet."