I've read about HIIT programs that have higher risk in suffering injuries but as I read further, I've discovered that one of the reason was the workout move was not done properly. They had not followed proper instructions as to how the move is to be executed. Example, burpees, if the posture is wrong, can damage your knees and causes strain to your lower back. So before starting any form of workout, study and read about the move before execution. Do some practice moves while facing the mirror to ensure the posture is right or get your training partner to check for you. This will lower the risk of any injury.
Getting good equipment is also a good step.
As of all workouts, there's always a training alternative. Alternative moves to facilitate beginners to first build their endurance. Example, Burpees alternative is Sprawls, Sit-Up alternative is Crunches.
From medical side of view, apparently doing the right exercise will help protects us from the injury. Example, if you have knee injury, by building the muscle around the knee joint will help decrease further stress. All in all, if you're still worried, do consult your own physician first before beginning any workout program.