The 21-year-old Wigan youth product has appeared in all but two of the Shrews' league and cup games this season and scored two goals.
"Jon is unlikely to be fit for the weekend," boss Graham Turner told the Shropshire Star.
"I think the early prognosis for him will be that it will be possibly two, maybe even three weeks."
If Turner's fears are confirmed, Taylor could miss out on the visits of Notts County and Oldham as well as the trip to Stevenage on November 30.
- Sports & Recreation
- Graham Turner