The home side are building towards their Championship opener against Norwich City on August 5, while Barnsley will begin their League One season at home to Port Vale on the same afternoon.
Match preview
Hull are back in England after a training camp in Turkey, which saw them play two fixtures, first beating Galatasaray 4-3 on July 5 before drawing 1-1 with Hatayspor four days later.
Liam Rosenior's side were also in action against Grimsby Town on Saturday, recording a 2-1 victory, with Regan Slater and Ryan Longman on the scoresheet for the Tigers.
The match against Grimsby consisted of four 30-minute quarters, with two different XIs taking to the field for an hour each, including an appearance for George Cox, who is on trial at the club.
Hull have made two signings this summer, bringing in Xavier Simons from Chelsea, while Liam Delap has arrived at the club on loan from Manchester City.
The Tigers, who finished 15th in the Championship last season, will follow this match with friendlies against Bradford City, Scunthorpe United and Nantes before opening their 2023-24 campaign with a clash away to Norwich on August 5.
Barnsley, meanwhile, are working towards their League One opener against Port Vale on August 5, with the team beginning their preparations for the new campaign by beating Worksop Town 2-1 at the start of the month.
The Tykes finished fourth in League One last season, which saw them qualify for the playoffs, but they were beaten 1-0 by Sheffield Wednesday in the final.
Barnsley will therefore again play in the third tier of English football next term, and there is a new face in the dugout, with Neill Collins becoming their new manager, replacing Michael Duff.
The third-tier side have made two signings during the summer, bringing in Ben Killip from Hartlepool United, while Kacper Lopata has arrived from Woking.
Barnsley have another three friendlies in the diary after this one, taking on Blackburn Rovers, Mansfield Town and Crewe Alexandra ahead of their first game of the season at the start of August.
Team News
Cox is again expected to be involved for Hull on Tuesday, with the defender currently on trial at the club following the expiration of his contract at Dutch side Fortuna Sittard.
Rosenior, as mentioned, used two different XIs for an hour each against Grimsby, and the Tigers head coach will again make full use of his squad in this match.
Oscar Estupinan is again expected to be a starter in the final third of the field, while Ozan Tufan should also be included in the home side's first XI on Tuesday.
Barnsley, meanwhile, are expected to have both Killip and Lopata in their squad, with the duo looking to make an impression following their recent arrivals.
Aaron Leya Iseka is also back at the club following a loan spell and could be given an opportunity to make his mark during pre-season.
Head coach Collins will make full use of his squad on Tuesday, but there should be some familiar faces in the starting side in the shape of James Norwood, Devante Cole and Herbie Kane.
Hull City possible starting lineup:
Ingram; Coyle, Jones, Fleming, Cox; H Vaughan, Woods, Seri, Tufan; Estupinan, Tetteh
Barnsley possible starting lineup:
Collins; Cundy, Cotter, Lopata, Williams; Kane, Moon, Phillips; Cole, Shaw, Norwood
We say: Hull City 2-0 Barnsley
Hull are ahead of Barnsley in terms of their preparations for the new campaign, and we are expecting the Tigers to triumph on Tuesday due to their superior quality, but it should be a competitive match at the MKM Stadium.