Most of the Roman world followed monogamy. In fact, the division between monogamous and polygynous societies tend to be geographic, rather than cultural, with polygyny being widespread in Asia and monogamy being centered in Europe (at the time of the first and second centuries).
Very ancient Greece was very likely polygynous, but by the times of the Golden Age and the empire of Athens, it seems to have been replaced by monogamy. Roman law tolerated polygyny among its conquered nations, but presumed that Roman citizens would be monogamous.
At a guess, as Christianity became (rather swiftly) a Gentile religion, taking its customs and mores from Rome, it simply adopted monogamy as the status quo, then made it law.