The injury comes at a bad time for the play-off chasing side, who sit one place and one point outside of the top four following the 13-13 draw with Munster at Thomond Park.
While Jones has only made five RaboDirect PRO12 appearances this season, his experience could have been vital as the Ospreys look to extend their season beyond May 3.
Wales assistant coach Robin McBryde said: "Ryan is not going to be available. He has broken a bone in his shoulder and he is now under the management of the Ospreys.
"It looks as though he will be out for six to eight weeks. Ryan has shown a great example to the other players in the squad and his leadership will be missed."