The South African-born 21-year-old will go under the knife this weekend to repair a cartilage problem in his right knee.
The Swansea-based region have already lost lock Alun Wyn Jones for up to four months with a shoulder problem, while tighthead prop Adam Jones is sidelined with a knee injury.
Ospreys head physio Chris Towers said: "We've spoken to several specialists and the view is that it is in Hanno's best interests to have the surgery now. We've taken a long-term view on what is best for Hanno's career moving forward.
"At this stage we are probably looking at a post-op rehab process of around five to six months, it's not something we can rush."