According to ESPNews, the initial diagnosis of Zambrano having "tennis elbow" was correct and he should make his next start.
They also, bizarrely, added that they though he got it hitting and not pitching. Gammons said that he takes extra batting practice and has a violent swing. Take that as you will.
Now I don't believe that he hurt himself just because of the 136 pitch start (one start won't do it, but cumulative effects will) but I doubt it was the hitting that did it. But if Zambrano really did hurt himself hitting, it would be a perfect summary with how awful and ridiculous this season has gone.