Usually, yes, it is a good idea to do them.

Bodyweight exercises will not put anywhere near the amount of stress on your body as weights would. It will allow you to keep active and ensure the muscle continues to get some sort of stimulation.

You should always do some light activities which don't effect your injured area, but be careful not to overwork ONE SIDE OF YOUR BODY compared to the other.

However, always ask your doctor if an exercise will cause any further damage, stop if you start to feel significant pain and be sure to REST it.

Related Questions:

1. If I suffer an injury to only one side of my body, should I continue to work the side that is still OK?
2. If I suffer an injury that stops me from lifting, should I do some other exercises instead? How long should I wait after an injury before I return to my normal weights?