Born in Mandatory Palestine, Nissim studied law at the Hebrew University of Jerusalem, gaining an MA. He was an Officer of Justice in the IDF during his national service, and went on to work as an attorney. He is the son of Rabbi Isaac Nissim, who served as Sephardi Chief Rabbi of Israel from 1955 to 1973. Moshe Nissim currently practices law at Moshe Nissim, Rinkov, Senderovitch, Advocates, in Ramat Gan, Israel.
Nissim was first elected to the Knesset in 1959 as a member of the General Zionists. However, he lost his seat in the 1961 elections, and did not reappear in the Knesset until 1969, when he was elected on the list of Gahal (a merger of Herut, the General Zionists and the Progressive Party). In 1973 Gahal became Likud, with Nissim serving as the party's parliamentary chairman between 1973 and 1977.