From a Seneca County, New York newspaper in March 1866:
FREE LIMBS. – Soldiers who have lost limbs in the service of the United States, are entitled to artificial substitutes, that can be procured upon the presentation of evidence of honorable discharge, and that the wound causing the loss of limb was received in the service. They are furnished free of charge, and do not affect any pension or bounty claim the soldier may have against the Government.
You can actually see a veteran fitted out with an artificial leg in a Photo Essay at The Civil War Monitor; however, the essay also points out that the empty sleeve became a badge of courage.