Btukfyl

I just watched "Fiddler on the Roof" and noticed Tevye said the following:

Who says he isn't? It's just that he's a different kind of man. As the Good Book says, "Each shall seek his own kind." In other words, a bird may love a fish, but where would they build a home together?

Presumably by "the Good Book" he meant the Tanakh however I am unable to find anything that resembles this quote in the Tanakh.

The two closest things that I was able to find were from the Book of Sirach

Sirach 13:15-19

15 All living creatures love what is like them,
and all people their neighbors. 16 All beings gather together with their own kind,
and people cling to those
who are like them. 17 What does a wolf have in common with a lamb?
So sinners have nothing in common
with the godly. 18 What peace is there between a hyena and a dog?
And what peace is there
between the rich and the poor? 19 Wild asses in the desert are prey for lions;
so the poor are feeding grounds
for the rich.

Sirach 27:9-10

9 Birds will nest with their own kind,
and truth comes back
to those who practice it. 10 A lion lies in wait for prey
just as sin lies in wait
for those who practice injustice.

However, I know that the Book of Sirach is not in the Jewish canon of the Tanakh so why would Tevye refer to it as "the Good Book"? That does not seem to really make sense.

In Bava Kama 92b, Rava asks Rabba bar Mari for the source of a popular saying along the same lines. Rabba bar Mari answers with five different sources for it. The third verse, which is attributed to "the Writings," is in fact the same verse from Ben Sira that you suggested as the source.

­­א"ל רבא לרבה בר מרי מנא הא מילתא דאמרי אינשי מטייל ואזיל דיקלא בישא גבי קינא דשרכי אמר ליה דבר זה כתוב בתורה שנוי בנביאים ומשולש בכתובים ותנן במתניתין ותנינא בברייתא כתוב בתורה דכתיב וילך עשו אל ישמעאל שנוי בנביאים דכתיב ויתלקטו אל יפתח אנשים רקים ויהיו עמו ומשולש בכתובים דכתיב כל עוף למינו ישכון ובני אדם לדומה לו תנן במתני' כל המחובר לטמא טמא כל המחובר לטהור טהור ותנינא בברייתא רבי אליעזר אומר לא לחנם הלך זרזיר אצל עורב אלא מפני שהוא מינו

Rava said to Rabba bar Mari: From where is this matter derived whereby people say: A bad palm tree strolls and goes to be among a grove of barren trees, [i.e., bad people seek out other bad people]? Rabba bar Mari said to him: This matter is written in the Torah, repeated in the Prophets, and triplicated in the Writings, and we learned it in a mishna, and we learned it in a baraita.

[Rabba bar Mari explains each of the sources.] It is written in the Torah, as it is written: “And so Esau went to Ishmael” (Genesis 28:9). It is repeated in the Prophets, as it is written: “And there were gathered vain fellows to Yiftah, and they went out with him” (Judges 11:3). And it is triplicated in the Writings, as it is written: All fowl will live with its kind, and men with those like him (Book of Ben Sira 13:17). We learned it in a mishna (Kelim 12:2): All that is attached to that which is ritually impure is ritually impure; all that is attached to that which is ritually pure is ritually pure. And we learned it in a baraita: Rabbi Eliezer says: Not for naught did the starling go to the raven but because it is its kind, [as it too is a non-kosher bird].

This passage in the Talmud may well be "the Good Book" you saw quoted.