Feinstein was appointed rabbi of Lubań, where he served for sixteen years. He married Shima Kustanovich in 1920, and had four children (Pesach Chaim, Fay Gittel, Shifra, and David), before leaving Europe. Pesach Chaim died in Europe, and another son, Reuven, was born in the United States. Under increasing pressure from the Soviet regime, he moved with his family to New York City in January 1937, where he lived for the rest of his life.

As one of the prominent leaders of American Orthodoxy, Feinstein issued opinions that clearly distanced his community from Conservative and Reform Judaism. He faced intense opposition from Hasidic Orthodoxy on several controversial decisions, such as rulings on artificial insemination and mechitza. In the case of his position not to prohibit cigarette smoking, though he recommended against it and prohibited second-hand smoke, other Orthodox rabbinic authorities disagreed. Even his detractors, while disagreeing with specific rulings, still considered him to be a leading decisor of Jewish law. The first volume of his Igrot Moshe, a voluminous collection of his halachic decisions, was published in 1959.

Feinstein died on March 23, 1986 (13th of Adar II, 5746). It has been pointed out that the 5746th verse in the Torah reads, “And it came to pass after Moshe had finished writing down the words of this Torah in a book to the very end.” (Deuteronomy 31:24). This is taken by some as a fitting epitaph for him.