The League One side will make the trip to Sussex after they were held to a 3-3 draw in the initial first-round meeting at Oakwell.
Match preview
Horsham are appearing in the first round for the second time in their history after they successfully negotiated their way through four qualifying rounds.
The non-league side subsequently earned an away trip to Oakwell, where they came from behind to establish a 2-1 lead thanks to a Shamir Fenlon effort and a James Hammond penalty.
Despite establishing a narrow advantage, they looked to be heading towards defeat after goals from Fabio Jalo and Mael de Gevigney put Barnsley in front.
However, Tom Richards proved to be Horsham's hero, tapping in an 81st-minute equaliser to take the first-round tie to a replay.
Since their trip to Yorkshire, Horsham have gone to thrash Chichester City 6-0 in the Sussex Senior Challenge Cup and lost 2-0 to Hashtag United in the Isthmian League Premier Division, but they will now turn their full attention back to FA Cup action, as they look to pull off a major upset and set up a second round tie against Sutton United.
Meanwhile, Barnsley head into Tuesday's cup tie off the back of a three-game winless run after playing out draws with Fleetwood Town and Horsham, before they fell to a disappointing 3-0 loss to Derby County at the weekend.
The Tykes had avoided defeat in their five league games prior to Saturday's trip to Pride Park, but that unbeaten streak was brought to an end by a James Collins brace and a Craig Forsyth effort.
While the result moved Derby level with Barnsley, Neill Collins's charges still managed to retain their place in the top six of the League One table.
The Barnsley boss will be concerned by his team's recent defensive displays, having seen his side concede two goals in each of their last three competitive games.
However, the Tykes are the joint-highest scorers in the third tier, and like the initial cup meeting, they will look to showcase their firepower against their non-league opponents.
Horsham FA Cup form:
Horsham form (all competitions):
Barnsley FA Cup form:
D
Barnsley form (all competitions):
W
D
W
D
D
L
Advert - content below:
Team News
Lewis Carey will start in goal for Horsham and the shot-stopper could be shielded by a back four featuring Bobby Price, Jack Strange, Doug Tuck and Harvey Sparks.
After coming off the bench to score the equaliser at Oakwell, Richards could be presented with a starting berth for the replay.
As for the visitors, Josh Benson could miss out after he was forced within six minutes of coming on as a substitute against Derby at the weekend.
Midfielder Herbie Kane is set to return to the lineup after serving a one-match suspension for yellow card accumulation.
Collins could also make a couple more alterations to his side, with Fabio Jalo and John McAtee likely to start the midweek fixture.
Horsham possible starting lineup:
Carey; Price, Strange, Tuck, Sparks; Fenelon, Hester-Cook, Barker, Brivio, Hammond; Richards
Barnsley possible starting lineup:
Killip; Williams, De Gevigney, McCart; O'Keeffe, Styles, Kane, Cadden; Jalo, Watters; McAtee