The 27-year-old crashed into the County boss while celebrating scoring a 65th-minute penalty in his side's 2-0 win on April 19.
The incident resulted in his sending off after he received a second yellow card for embroiling himself in a tussle with various opposition players and staff.
He will now miss Hearts' final game of the season against St Mirren this Saturday after the Scottish FA found him guilty of excessive misconduct.
Hamill has already served one of the four games, the 2-1 win at Hibernian on April 27, and another match has been suspended until the end of the 2014-15 season.
In a statement, the SFA said: "Jamie Hamill was found in breach of Rule 201; Excessive Misconduct.
"Mr Hamill has received a four-match suspension, one of which has already been served and one suspended until the end of season 2014/15 if he breaches Rule 201 again."
Hamill has made 40 appearances for the relegated Scottish Premier League side this season, scoring nine goals.