City beat the Tykes 2-0 in the FA Cup fifth round back in 1993 thanks to two David White goals - the only time the teams have previously met.
The in-form South Yorkshire side, now coached by former City star Garry Flitcroft's brother David, are sure to bring 6,000 fans for what is likely to be another sell-out tie.
Ticket details will be announced shortly. The tie will take place on either 9/10 March.
The full draw is:
FA Cup 6th round sponsored by Budweiser
Oldham or Everton v Wigan Athletic
City v Barnsley
Man United or Reading v Middlesbrough or Chelsea
Millwall v Blackburn Rovers