Even though a lot of the book has Tevye bemoaning his general unluckiness, and milking his whole martyr/Job complex, we gradually get the sense that the real villain isn't a specific person—or even God—but the oppressive political conditions that Tevye and the other shtetl Jews live under.
We catch glimpses of this early on—like when Menachem-Mendl has to sneak around in order to be a broker in Yehupetz because he's not legally allowed to live there because of a quota on the Jewish population. "Come," he says, "I'll tell you what it means to be a resident and not a resident" (3.20).
Later, it's clear that there is something especially horrible for Tevye in Chava's decision to marry a non-Jew, because it connects her with the culture that is responsible for so much of Jewish torment. (Example: he uses the phrase "Do not open your mouth to the devil" [6.80]) when Chava tried to get him to talk to the priest.)
And in the end, the government passes a decree to expel Jews from the village and to seize their property, even as officials stand by (and frequently encourage) the pogroms that are raging across Jewish neighborhoods and villages in Russia. Tevye sells his house and his horse, the two things that symbolize his identity (check out "Symbols" for more about that).
So, yeah, that's the real enemy here.