Lots of people are injured doing their favorite aerobic activity. Whether it's a sprained ankle, runner's knee, IT Band Syndrome, etc., it is important that you give your body proper time to heal. Always (obviously if it's serious) talk to your doctor and trust him/her about when to continue exercise.
Be encouraged though, most injuries and the new treatment techniques that are now available allow for a quick recovery time and call for you to continue a modified version of the exercise to promote proper healing.
However, if you are forced to sit on the sideline from aerobic or weight bearing exercise, think of it as a new challenge to get back to where you were. I see more results after starting up again as it actually allows for all of your soft tissues to get a full recovery.
For lots of people aerobic exercise injuries are a result of bad posture, and for aerobic exercise it is generally in reference to our lower body. Flat feet, knees that come together and lower back rounding are all good causes of why we might hurt ourselves in an aerobic activity setting. So, here are some interesting ways that we can strengthen our lower bodies in a functional way.
We've all seen a treadmill. Try walking backwards on it! This is going to give you a great workout for your glutes and hamstrings while also strengthening the muscles in your feet. Make sure that as you walk backwards you're extending back far with your legs, standing nice and tall, while making sure you are stepping equidistantly back with both legs.
Start slow and hold on to the side rails but eventually when you get more comfortable, let go of the sides. This will allow for you to fully engage your postural muscles.
Also try walking sideways on the treadmill (switching directions halfway) to exercise your adductors (inner thighs) and abductors (outer thighs), while also strengthening the muscles in your feet. See a trend? If you stress your feet to function in awkward movements, you will be training them to be strong and firm, and in most cases help prevent more injury while still allowing for great recovery and long-term benefit.
Can't find a treadmill? The ground will work just fine too!