Mowbray admitted a charge of improper conduct and using abusive and insulting words towards referee Nigel Miller at the end of last month's Championship clash against Sheffield Wednesday at The Hawthorns.
The FA's disciplinary committee ruled that because of the former Hibernian manager's exemplary record, his punishment should be suspended until the end of the 2008-09 season.
Mowbray had marched onto the pitch after the final whistle to confront Miller after the Owls had grabbed a controversial late equaliser against his side.
He had fumed: "Where do you start? I've got to be careful, he's already told me he'll be reporting the conversation but I think an injustice has been done.
"For me it's a blatant foul and the fourth official is telling me that time is finished. It was over by three minutes when we got a goal-kick.
"Our game has got the best referees in the world, but this is very hard to take. There were some strange decisions."