Hibbard was on the bench as Wales defeated Scotland 51-3 to end their RBS 6 Nations campaign on a high.
International team-mates Sam Warburton and Leigh Halfpenny have also seen their season ended by shoulder injuries in recent weeks with Ospreys medical performance manager Chris Towers believing surgery is the best option for Hibbard.
"Richard has an ongoing shoulder problem that has been troubling him, and after returning to the region this week he feels unable to continue playing," said Towers.
"It is in his best interests to get this issue resolved and he will undergo surgery today. The expected minimum recovery time for such a procedure means it is unlikely he will play again between now and the end of the season."