The 24-year-old full-back, who signed on loan from Oldham in January, was shown a straight red following a challenge on Saddlers defender James Chambers but, having viewed the replay several times, Jackson has requested a review of the decision.
"We've had a look at it over the weekend, and a few other people have as well, and we feel there is a case for it to be reviewed," the Shrews boss told the club's official website.
"We've filled in the paperwork and sent over the footage which will now be reviewed and we should get an answer late on Tuesday.
"It would be a blow to lose Joseph for three games so hopefully the review will go in our favour and he will be available for the Stevenage game."
Should the FA opt to deny the appeal Mills will be unavailable for the games against Stevenage, Tranmere and Crewe.