To "be recovered" means that your injury or sickness has healed.
The word "recovered" can refer to either the body part:
Is your shoulder recovered?
Or it can refer to the person:
I'm glad to see that you're recovered.
You could also say:
The question is whether his leg has fully recovered.
In fact, "has recovered" is probably more common than "is recovered":
Has your shoulder recovered?
I'm glad to see that you've recovered.