The Jambos lost 2-0 in the Highlands while they were also reduced to 10 men late on as Hamill was dismissed by referee John Beaton for a handball in the box.
But television replays showed Billy McKay's shot hit the Gorgie man flush in the face.
Now a Hearts spokesman has confirmed the club hope to have the dismissal overturned.
He said: "We are appealing the red card shown to Jamie and hope to have him available for the Celtic game on September 14."
Mackay struck twice as Caley Thistle collected the three points on Saturday to maintain their position at the top of the Scottish Premiership table.