The Owls and Carlisle will meet again in the third round of the FA Cup following the 0-0 draw at Brunton Park on Saturday.
The replay at Hillsborough will take place on Tuesday 16 January (7.45pm) and ticket details will be confirmed in due course.
In the meantime, the draw for the fourth round will take place on Monday 8 January.
Wednesday and Carlisle will be in the hat and represented by ball number 32.
Supporters can watch the draw live on BBC 2 and BT Sport from 7.10pm.