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Souness will have to watch Rovers next away match from the stands – at the Premier League fixture with Middlesbrough.
The disciplinary action comes after Souness attended a personal hearing and pleaded guilty to the charges.
Rovers exec. John Williams said: "Graeme asked for a personal hearing, got it and apologised for the incident. He had already pleaded guilty as charged. We feel that we got a fair hearing.
"Graeme will sit out the Middlesbrough game but we don’t believe it will affect the team’s performance."