A Rugby Football Union disciplinary panel suspended Gillies until April 26, meaning he will miss Sunday's Premiership trip to London Irish.
He is free to play again on April 27.
RFU disciplinary officer, HHJ Blackett said: "The sending-off was a mid-range entry point offence which carries a recommended sanction of five weeks.
"However, we gave Craig credit for his good character and the circumstances of the incident and consequently imposed a maximum reduction of three weeks.
"We gave him a one-week ban for the citing (for stamping) but because this incident and the red card were 15 seconds apart and, in effect, the same phase of play, the panel decided the suspensions should run concurrently rather than consecutively."