The 19-year-old winger was shown the first red card of his professional career late on in Saturday's 1-0 win at Morecambe following a clash with Garry Hunter.
Taylor will now miss the encounter against Vale as well as Saturday's home match against Aldershot and the subsequent trip to Macclesfield on Good Friday.
That will force Graham Turner into a change out wide although the Town boss is otherwise expected to keep faith with the same line-up following back-to-back wins over Plymouth and the Shrimps.
Shrews picked up no new injuries at the weekend and go into the encounter in third place, a point behind Torquay in second, although leaders Swindon and fourth-placed Crawley boast an extra game in hand due to their cup exertions this season.
Port Vale teenager Joe Davis is suspended for the trip to Greenhous Meadow.
Davis was sent off midway through the second half of the 2-1 defeat at Torquay on Saturday and will serve a one-match ban. Clayton McDonald will make a timely return from his two-match ban to replace Davis at centre-half.
Manager Micky Adams admits Vale's tough fixture schedule, as they prepare for their seventh game this month, is beginning to take its toll on some players including recently-signed midfield duo Paul Marshall and Chris Shuker.
Senior centre-back John McCombe is likely to play on despite continuing to suffer with a rib injury and back spasms while winger Rob Taylor will be assessed after missing out at the weekend with an Achilles injury.
"I can see the games are taking their toll," said Adams. "I left Paul Marshall out on Saturday to give him a breather because I felt the pace of the games was catching him up. Chris Shuker also hasn't played much football in recent months, but he has played a number of games and picked up a hamstring injury.
"That is down to over-working so we will have to monitor the situation. We haven't got any bodies that we can throw into the squad, but maybe people who have sat on the bench recently will be given their chance now."