Also missing for the trip to Italy, where the Ospreys have already tasted RaboDirect PRO12 success back in September, will be hooker Huw Bennett who suffered a neck spasm against Biarritz last Saturday.
Ospreys head physiotherapist Chris Towers said: "Alun Wyn suffered a foot injury in training this week and as a result, he is going to require surgery to repair soft tissue damage, which will be carried out over the weekend.
"Once he starts his post-op rehab work we will be in a better position to predict recovery timelines.
"Huw, unfortunately, didn't recover in time from a neck spasm that developed after last weekend's game to be considered to play against Treviso."
A likely replacement for both games is versatile 30-yeart-old Ryan Jones, while fellow Welsh cap Justin Tipuric is set to undergo a fitness test ahead of the Stadio di Monigo clash.