However, he has been discounted one match having already sat out the Edinburgh derby win over Hibernian as a result of the automatic suspension which followed his red card for the bizarre incident involving the Staggies boss.
Another match has been suspended until the end of next season.
That means Hamill will miss the already-relegated Jambos' final game of the season against St Mirren on Saturday and the first game of next season's Championship campaign.
The 27-year-old sent Adams sprawling with a shoulder barge just seconds after scoring a penalty in the Jambos' 2-0 win on April 19.
The former Kilmarnock man was then shown a second yellow card by referee Willie Collum.
But the Scottish Football Association's compliance officer Vincent Lunny decided the incident required further punishment and issued Hamill with a notice of complaint.
The governing body's disciplinary panel found Hamill guilty of "excessive misconduct".