He will miss the games against Real Madrid and Galatasaray but can return to face Club Bruges on 22 October.
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Cas says it will publish the reasons behind their ruling in a few weeks.
Neymar was injured with a broken metatarsal and missed both legs of the tie against United.
Referee Damir Skomina reviewed footage of a Diogo Dalot shot striking the hand of PSG defender Presnel Kimpembe before awarding the visitors the injury-time spot kick having initially given a corner.
Marcus Rashford’s penalty ensured a 3-1 win in Paris for United, who went through to the Champions League quarter-finals on away goals after the tie ended 3-3 on aggregate.
Neymar wrote on social media: “It’s a disgrace. Four guys who know nothing about football watch a slow-motion replay in front of the television.
“What can he do with his hand while his back is turned?”