The body apologised for “the confusion and inconvenience caused”.
The Games will conclude on Sunday with a closing ceremony at Stade de France, the venue for the track and field events.
The CAS ad-hoc division, established specifically for dispute resolution during the Games, accepted Vinesh’s appeal against her disqualification on Friday.
Vinesh is requesting to be awarded a joint silver medal with Cuban wrestler Yusneylis Guzman Lopez, who was promoted to the final after Vinesh’s disqualification, despite having lost to her earlier.
American Sarah Hildebrandt claimed the gold after defeating Lopez in the final.
Vinesh was represented by prominent senior advocates Harish Salve and Vidushpat Singhania.
Devastated by her disqualification, the world championships bronze-medallist announced her retirement on social media.
The United World Wrestling has already stated that it is not inclined to make an exception for her, though it may consider rule reforms in the future. International Olympic Committee (IOC) president Thomas Bach has expressed a similar stance.
India concluded the Games with six medals: one silver and five bronze. Two of the bronze medals were won by pistol shooter Manu Bhaker, while the lone silver was secured by Neeraj Chopra, the defending champion in men’s javelin throw.