He was cited by independent citing commissioner James Hall following the Bath v Saracens fixture last Friday.
This was for making contact with the head of Levi Douglas in a ruck contrary to Law 9.20(a) - dangerous play in a ruck or maul.
The incident occurred in the first half.
Rhodes accepted the charge and was given a three-week suspension by the independent panel comprising Daniel White (chair) with Paula Carter and Nick Garling.
He is free to play again on April 2.
Panel chair 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.
"The panel considered the actions of the player in detail and were assisted by hearing the player's account of events as well as reading the detailed citing report.
"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 for the reasons which will be explained within the detailed judgment.
"We gave the player the maximum permissible credit of 50% 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."