The Owls will be the second League One side the Iron have hosted in the competition, having come from behind to defeat Oldham Athletic in the first round 2-1 last week.
Wednesday reached the second round thanks to a 1-0 home win over the League Two side Bury.
Tickets will be priced from £12-£17 for adults, with season ticket holders who reserve their seats in advance able save up to three pounds. The match will kick-off at 7.45pm and has not been chosen for live TV coverage.