Both McCann and Gerrard were charged with a breach of rule FA Rule E3, alleging they used abusive and/or insulting words towards a match official in or around the tunnel area following the controversial draw with Charlton Athletic.
The pair accepted the charges and requested a hearing to air their views, which was held via videolink from the Keepmoat Stadium on Thursday afternoon.
Following the hearing, the FA's disciplinary panel handed down a one-game ban for both, plus a fine of £1,000 for McCann - understood to be the lowest grade punishment at their disposal.
It means McCann and Gerrard will be absent from the dugout when Rovers host neighbours and promotion rivals Barnsley in Friday's televised clash.
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The incident which brought about McCann and Gerrard's charges saw Rovers have a last minute winner ruled out for offside against Charlton.