Hassell was carried off just 5 minutes into last night's 1-1 draw at Bournemouth which moved The Reds into 3rd place and was replaced by Paul Reid.
Losing Hassell who has been one of Barnsley's most consistent players this season will be a big blow as the Reds launch an assault on the automatic promotion places.
Andy Ritchie told www.barnsleyfc.co.uk:
"The good thing for us is that Bobby was not kept in hospital overnight. It looks as though he has three broken ribs and he was really struggling to breathe when he came off. We will know more when we have him x-rayed again on Wednesday".