The 55-year-old received the punishment - as well as an extra game’s ban suspended until the end of 2019 - following a Scottish Football Association disciplinary hearing.
The Killie boss will be in the Rugby Park stand as his team bid to secure third spot in the Ladbrokes Premiership and a guaranteed Europa League place.
His trip to Hampden came as the SFA close in on an appointment for the vacant Scotland manager’s role with Clarke among their main preferred options.
Clarke was charged with making criticism of a referee which might indicate bias or incompetence or impinge on his character after calling for Steven McLean never to referee another Kilmarnock game.
The former Scotland defender spoke out after his team had three players sent off during a 1-0 defeat by Aberdeen on April 20. Rory Mckenzie’s red card was later rescinded.
He said after the game: “I went over and congratulated him (McLean) and told him it was the worst performance I had ever seen in my career - and it is a long career.
“He lost control of the game in the first half. He actually lost control of a professional football match.
“When we lost 2-1 to Hearts earlier in the season I mentioned the referee that night and it was Steven as well. And he didn’t control that game properly either.
“I feel a little bit sorry for him. People tell me historically that he has never been particularly kind to Kilmarnock.
“I think he feels the pressure of the fact that his father played so many games here. I really do.
“I have mentioned it a couple of times privately but publicly I am saying now, I think it would be better for Steven and Kilmarnock if Steven doesn’t referee any more games for us. Quite simple.
“It is a big family connection. Stuart McLean was a top, top player here. I remember coming to watch him.”
Clarke received a suspended two-match ban earlier in the season following criticism of the SFA’s disciplinary procedures, but the charge was only proved in relation to a different rule and the new offence will not trigger the punishment.
In an eventful week for the former Chelsea defender, Clarke was earlier named Scottish Football Writers’ Association manager of the year.
He saw off competition from Scotland women’s boss Shelley Kerr, Livingston manager Gary Holt and Arbroath’s Dick Campbell to take the award for a second season running.
Clarke was also voted top manager this month by his counterparts in the Scottish league.