Hacham Yitzhak Salah Machmal was born to Freicha and Salah on 13 Tishrei 5636, in Baghdad, Iraq. He first studied at the Midrash Talmud Torah, and then at the Beit Zalicha yeshiva with Hacham David Ben Meir Maatuq and Hacham Shimon Aharon Agassi.
His father died in 1898 when he was 23 years old, and his mother began to support the family so that he could be free to continue his Torah studies.
In 1905, Hacham Machmal immigrated to the Land of Israel with his entire family. They visited holy sites and resided in Jerusalem for several months, but because of Hacham Yitzhak Salah Machmal's poor health, they soon returned to Baghdad.
In 1906, Hacham Yitzhak Salah Machmal began to teach Bible, Talmud and Hebrew language at the Midrash Talmud Torah. As of 1926, he was also giving evening classes in Hebrew, grammar and Jewish history. In 1942, he volunteered to train teachers who taught Hebrew and Judaism in the community's afternoon school on a voluntary basis, and in addition to his work at school, gave Talmud lessons in local synagogues.
Hacham Yitzhak Salah Machmal immigrated to Israel with his family in 1950, along with the Jewish Iraqi community. Poor housing conditions exacerbated his failing health, and he died while still in the transit camp, on 4 Sivan 5711 (1951), a Sabbath Eve. Word of his death spread rapidly, and he was mourned by the Jewish immigrants from Iraq throughout Israel.
Hacham Yitzhak Salah Machmal was buried in the Jerusalem's Har Hahamenuhot cemetery.
He is the author Davar Be'ito, a book of sermons for various festivals and occasions, Netivot Yitzhak, and additional booklets on the Hebrew calendar and leap year system, and of various publications on remedies, amulets, ethics, and grammar.