The Tykes can haul themselves out of the bottom three with victory at Oakwell over Hull, who will secure automatic promotion to the Premier League if they win.
A South Yorkshire Police statement read: "We understand the passion involved in football especially at such a crucial time and therefore everyone is working hard to ensure the match runs smoothly in and around the ground.
"Due to the significance of this match for both teams, an increase in the number of police officers present around Barnsley town centre will be apparent on Saturday in order to ensure the match passes with minimal disorder."
Temporary superintendent Scott Green, police commander for Saturday's match, added: "We appreciate the passion involved in supporting a football club and welcome friendly rivalry, especially in the last home game of the season.
"Unlike previous years, I'm asking the Barnsley fans to remain in the stands and not go on the pitch after the final whistle.
"We understand that this has become a tradition in previous years. However, Barnsley players will not be coming back out unless the pitch is clear.
"Anyone entering the pitch may be arrested and South Yorkshire Police may additionally seek a football banning order. So please don't spoil it for yourselves and others."
- Sports & Recreation