The Uruguay internationalist was suspended from all football-related activity for biting Italy defender Giorgio Chiellini at the World Cup, with the punishment also including a nine-match international suspension and a £66,255 fine.
Suarez, the Uruguayan Football Association and Barcelona - who spent £75m to sign the striker from Liverpool this summer - appealed to CAS over the severity of the punishment and a number of restrictions have now been lifted.
He will not be able to play a competitive game until the clasico against arch-rivals Real Madrid on October 26 but he will be able to train and feature in friendlies.
Barcelona's priority was to have Suarez available to work with the team, important in pre-season but essential for a new player, and CAS have relented on that issue.
The panel said: "The stadium ban and the ban from "any football-related activity" were excessive given that such measures are not appropriate to sanction the offence committed by the player and would still have an impact on his activity after the end of the suspension."