Hamilton was given the ban by a Rugby Football Union (RFU) disciplinary panel at Twickenham on Tuesday and will be available to play again Monday, December 15.
The loss of Hamilton is another blow to the Tigers, deprived already of many of their first-rank players who are on World Cup duty in Australia and suffering a major slump in form in the Zurich Premiership.
Hamilton, 20, has made a total of six Premiership appearances for his club this season, receiving the red card in the 16th minute of the 39-18 defeat to Leeds.
