The Leicester skipper was cautioned during the Tigers' matches with Bath and Bristol on successive weekends.
He was sin-binned last Saturday for tackling Bristol flanker Micahel Lipman without the ball.
Under English rugby's totting-up procedure, Johnson's third yellow card in a 12-month period means he faces a one-game domestic ban.
Tigers coach Dean Richards complained after Saturday's game that Johnson was 'being refereed differently to other players.'
Unless he wins his appeal, which will be heard in Yorkshire on Monday week, he could miss Leicester's Powergen Cup semi-final against Gloucester the following Saturday.
Sale Sharks prop Kevin Yates will also be dealt with by a Rugby Football Union disciplinary panel on the same evening.
Yates was cited by the independent match commissioner for alleged dangerous tackling and punching during Sharks' Premiership victory at London Irish 12 days ago.
Another RFU panel will sit in Wycombe the following night to deal with three additional citing cases.
Saracens' Australian World Cup-winning centre Tim Horan must answer a charge of punching in a Premiership game against Gloucester.
Gloucester's Robert Todd has also been summoned for a dangerous tackle that left Saracens scrum-half Kyran Bracken concussed.
Harlequins flanker Ace Tiatia, meanwhile, has been reported on a charge of playing an opponent without the ball when Quins lost at Newcastle earlier this month.