City manager Nigel Pearson told BBC Radio Humberside he intends to get to the bottom of the problem.
Pearson said: "I think the next step for him is to have an exploratory operation. He's got a little bit of history with knee injuries."
The Tigers were expecting the 29-year-old Garcia to be away from the club on international duty for his country, but that will not now happen according to Pearson.
"He looked like being called into the Aussie squad, so we could have been missing him anyway, but it looks like we'll be missing him for a different reason now," he said.
"It's a real shame because I think during our more difficult times he's been one of our really reliable performers, and he's a player that gets on with the job - whichever job you ask him to get on with."
Earlier this year Garcia became the first Hull City player to take part in a World Cup, when he was selected by Australia to start in their group game against Germany.
Source: BBC Sport
Source: BBC Sport