The Ireland winger and full-back sustained the injury in their win over Scarlets last weekend in the PRO12.
Zebo will be joined on the sidelines by hooker Kevin O'Byrne who is out for three months with an elbow injury.
Meanwhile, Jaco Taute joins the province on a four month loan basis, subject to being granted a valid work permit.
The Stormers and Western Province centre/fullback played for the Springboks on three occasions in 2012 and has made 50 Super Rugby appearances, having also represented the Lions.
Director of Rugby Rassie Erasmus has made just two changes for tomorrow night's Pro12 clash with Cardiff Blues at Irish Independent Park.
The first change is seen in the half-backs with Ian Keatley coming in to partner Duncan Williams.
The final change is at full back where Andrew Conway makes his first appearance of the season.
Tipperary's Dave Foley and Tommy O'Donnell have retained their places.
Returning international CJ Stander is named among the replacements, as is Nenagh native Donncha Ryan.
