Hamilton and Paice were both sent off for striking in the Aviva Premiership match between the sides at the Madejski Stadium on May 5.
Hamilton's suspension runs until August 19, covering Scotland's warm-up and tour matches this summer, and warm-up games at the start of next season.
Paice's suspension runs from August 10 to September 13 next season.
The panel of His Honour Judge Jeff Blackett (chair), Robert Horner and Jeff Probyn considered that both offences required top-end entry points because they were committed after the players had been issued yellow cards.
Both players have a right of appeal.
Gloucester Rugby will be making no further comment at this stage.