Nsiala, 24, was dismissed for his foul on Swindon's Luke Norris in Saturday's 1-1 draw - just six days after joining the League One club from Hartlepool.
But Town are confident of winning the appeal, boss Paul Hurst claiming: "It's never a two-footed challenge.
"He clearly wins the ball. We've looked at the footage," he told BBC Sport.
Nsiala had already been sent off twice for Pools this season, which automatically increases the punishment, potentially sidelining him until 11 February.
Unless Shrewsbury win their appeal to the Football Association, Nsiala will miss the visits of Bradford City, Oldham Athletic and Bury, as well as the trip to Gillingham.
His home debut may not now come until 18 February against AFC Wimbledon.
The red card was the eighth Shrewsbury have received this season - the highest number in English football's top four divisions.
Meanwhile, Shrewsbury have allowed former Wolves striker Sylvan Ebanks-Blake to return to Chesterfield at the end of his loan spell, during which he failed to score in seven appearances.
They have also allowed on-loan winger George Waring to return to Premier League side Stoke City, having opted not to extend his deal.
Hurst has also dismissed speculation linking the Shropshire club with striker James Alabi, National League side Chester's 10-goal top scorer, saying: "There's no truth in it."
Shrewsbury defender Aristote Nsiala will be banned for four games after being sent off on his debut - unless the Town are successful with an appeal.