The Owls will face Hartlepool United on Wednesday 1 December in the second round of the Papa John’s Trophy.
Kick off at Hillsborough will be at 7.00pm.
The draw was made on Saturday lunchtime and Wednesday were paired with Pools, who are currently 10th in League Two.
Darren Moore’s men qualified for the next stage having topped Group H with maximum points after victories over Newcastle Under-21s, Mansfield and Harrogate.
Hartlepool finished as runners-up in Group A.
Ticket details will be released in due course.