The football club said the group - ‘Rainbow Reds’ - will be open to all supporters and that anyone interested should follow the ‘@RainbowReds’ Twitter page for more information.
Once a number of supporters are involved, it is hoped the group will host regular events and grow as a community of support.
The announcement came on Rainbow Laces Day - an event which celebrates the LGBTQ+ community in football - when the club lit up the South Stand with rainbow lighting ahead of the Sky Bet Championship game against Swansea City.
Other demonstrations of support on the day included a rainbow-coloured captain’s armband worn at first team, under 23s and under-18s level and rainbow corner flags displayed at home fixtures.
A spokesperson said: “Discrimination of any kind is not tolerated or welcomed at Oakwell.
“Barnsley FC will continue to strive for change and ensure that Oakwell is a safe place for everyone.
“If you see or hear discrimination at or during a Barnsley FC fixture, text us in confidence on 60777 and start your message with ‘HATE’.”