Rhodes received a three-week ban following a citing for dangerous play in a ruck or maul during his side’s Gallagher Premiership defeat at Bath last Friday.
He was reported for making contact with Bath lock Levi Douglas’ head during the first half.
Rhodes appeared before an independent disciplinary panel, when he accepted the charge. He cannot play again until April 2.
In addition to the Glasgow game on March 30, Rhodes must also sit out the Premiership appointment with Harlequins next week.
In a statement released by the Rugby Football Union, panel chairman Daniel White said: “The player accepted that he had committed an act of foul play in that he made contact with the head of the Bath player.
“Actions such as this have the potential to cause serious injury, albeit in this case no injury was caused.
“The World Rugby sanction table mandates that when contact is made to the head, such as was not disputed in this case, we must use the mid-range entry point or above. We did not consider that this case merited a top-end entry point.
“We gave the player the maximum permissible credit of 50 per cent on account of his acceptance of the charge, his record (which included only one previous disciplinary matter from 2011 and was not considered relevant for the purposes of this hearing) and his remorse shown, and in so doing impose a total sanction of three weeks’ suspension.”