The Ravenhill outfit have had a tough few weeks, losing 44-16 to Connacht on December 23, and despite winning 24-17 at home to Munster, were crushed 38-7 at Leinster on Saturday.
Bowe was forced off in the six-try rout in Dublin and it has now been confirmed he faces a spell on the sidelines.
The 33-year-old's injury is expected to end his hopes of a recall to the Ireland squad for the Six Nations having missed out on the November Tests.
Kiss confirmed the blow after the defeat at the RDS and has predicted that the former Osprey, who also toured with the British & Irish Lions in 2009 and 2013, will be out for up to eight weeks.
"It looks like it's around the sternum but we're doing more tests," said Kiss.
"The doc said weeks so that could be anything getting up to eight. That's a shame for him."