Southend, who are in League One like the Reds, drew 1-1 at home to League Two Crawley over the weekend.
The game is due to be played on the weekend of November 30 to December 2. Barnsley won 4-0 at home to Notts County in the first round on Saturday, their first FA Cup victory since 2014.
This will be their first appearance in the second round in four years since they were held to a 0-0 Oakwell draw by non-league Chester before winning 3-0 away on BT Sport.
Head coach Daniel Stendel has targeted at least the third round when the Championship and Premier League sides enter the competition.