Webb made 15 appearances in the GUINNESS PRO12 last season as the Welsh region were knocked out in the play-off semi-final.
This season former All Black Brendan Leonard has stepped into the No.9 shirt in Webb's absence but the loss of the 26-year-old will be an undoubted blow.
Chris Towers, medical performance manager at the Ospreys, confirmed:
"Rhys sustained a significant foot ligament injury that required surgical stabilisation. He has had the surgery and will be non-weight bearing for six weeks and will then wear a protective boot for a further four to six weeks.
"Only after that will we be in a position to progress his rehab and, at this stage, Rhys is looking at a six to eight month period out of action, a timescale that reflects the severity of his injury."
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