It could be one of the civilian hospitals in the United Arab Emirates. It could be in Qatar. It could conceivably be a hospital in Pakistan. Depending on the injury, it would be wherever the most appropriate type and level of care is available.
There's a process that kicks in from there, involving 1 Canadian Air Division in Winnipeg as well as the medical personnel, to arrange for the evacuation of the individual. If it's a minor injury they tend to be booked on commercial airlines, either with or without an escort. If it's something more serious that requires medical care while they're in flight, then for single individuals it tends to be the Canadian Forces Challenger aircraft. Occasionally we will lease air medical evacuation capabilities. They do exist in the commercial sector.
More specific examples are probably best addressed by the director of health services operations.