The Old Trafford encounter is to take place on Tuesday 17 September at 20:00 BST.
It is being broadcast on Sky Sports Football, while the rest of the evening's matches are being shown on Sky Sports +.
Tickets are available to buy here.
Barnsley defeated Sheffield United 1-0, at home, in the second round of the competition and travel to Old Trafford for the first time since 1998.
The Carabao Cup meeting will be the 39th match between the two sides, with United winning 22 of the previous contests.
There are further third-round fixtures on Wednesday 18 September and more the following week, on Tuesday 24 and Wednesday 25 September.