The Confédération Africaine de Football (CAF) Disciplinary Board have punished Mamelodi Sundowns and Orlando Pirates, including two players.
Pirates and MC Alger players and officials had to be separated after the second leg of the quarter-final on 9 April at Orlando Stadium, while there was also a pitch invasion from the supporters.
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For the scuffle after the game, Pirates players Sipho Chaine and Nkosinathi Sibisi were handed one-game bans, both of which are suspended for one year.
Buccaneers team doctor Ezekiel Matebula has been given a four-game ban, two of which are suspended for one year.
On top of the suspensions, the Soweto have also been fined $50 000 (R940 990) for improper conduct and $20 000 (R376 394) for failing to provider adequate security.
Sundowns, meanwhile, have been found guilty of breaching Article 82 and 83.2 of the CAF Disciplinary Code after the supporters clashed in the stands at Loftus Versfeld on 1 April.
The Brazilians have been ordered to pay a fine of $100 000 (R1.8million) and must implement safety and security measures specified in the CAF regulations for upcoming matches.
Both Pirates and Sundowns will be at home in the first leg of their Champions League semi-finals against Pyramids FC and Al Ahly respectively.