Butcher chose not to challenge the suspension offered by the Scottish Football Association following his criticism of referee George Salmond, and will be absent from the dugout when Ross County visit the Tulloch Caledonian Stadium on Friday night.
Butcher was charged with "making comments in a media interview which criticise a decision of the referee in such a way as to indicate incompetence" following the 1-1 SPL draw with Aberdeen on September 15.
The former England captain criticised Salmond's decision to show Owain Tudur Jones a straight red card for a challenge and felt his side should have been awarded a second penalty when Mark Reynolds challenged Aaron Doran in the box.
The Caley Thistle manager said: "I spoke to the referee afterwards and he said Aaron Doran scuffed his shot before falling over.
"However, he's the only man in the planet who saw that. In fact a Martian could have seen it all the way from Mars."
The SFA later repealed Aberdeen defender Russell Anderson's red card for a challenge that led to Caley Thistle's penalty.