The club have said in a statement they will appeal on the grounds the incident that left Northampton wing George North unconscious and resulted in a red card for Hughes was an accident and no foul play had occurred.
With the hearing scheduled to be heard next Friday, it means Hughes can not be reprieved in time to face the reigning European champions in Toulon this weekend.
Hughes was given the suspension - to include three meaningful fixtures - after being found guilty of striking North in the 52-30 Aviva Premiership defeat at Franklin's Gardens on March 27.
Commenting on the judgement made on Tuesday night, disciplinary officer Sir James Dingemans said: ''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.''