The tie at the Arden Garages Stadium will take place on Sunday, November 7 (3pm kick-off) and broadcast live on ITV4.
Stratford pulled off a famous victory, taking down Boston United in a 3-2 thriller on Tuesday night.
Live TV coverage has also guaranteed the Bards & Shrewsbury a £50,000 windfall.
Steve Cotterill's men will be hoping a good cup run will change their fortunes with Salop currently 21st in League One.
Ticket details will be released in due course.