Hughes was sent off after colliding with Northampton's George North in an English Premiership match on March 27.
Wales winger North, 22, was knocked unconscious and received lengthy treatment before being taken off on a stretcher.
North, who sustained two head injuries in Wales's Six Nations game against England last month, was injured as he scored Northampton's second try in a 52-30 victory.
The 23-year-old Fiji-born forward Hughes was found guilty of "striking with the knee and/or shin, contrary to Law 10.4(a)," the RFU disciplinary panel announced in a statement.
The player and his club had denied the charge.
Hughes will not be free to play again until April 28 which would mean the number eight also missing the semi-final if Wasps prevail against the defending champions in France.
“This was a three-week ban on the basis that no intention was found. However, there was recklessness meaning that, notwithstanding the harm, it was a low entry point of four weeks with mitigation of one week to reflect his previous clean playing record.” said the RFU disciplinary panel.
(Editing by Toby Davis)
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