The Labour Party's Galeb Magadla becomes minister without portfolio in the coalition government of Ehud Olmert, the prime minister.
Magadla told Israeli Army Radio following the vote that the move would help Israel's Arab citizens identify more strongly with the Jewish state.
He said: "The first step has been taken and this has given Israeli Arabs a feeling of belonging."
Güncelleme Tarihi: 20 Eylül 2018, 18:16
A senior government source said all ministers except for Avigdor Lieberman, the ultra-nationalist minister of strategic affairs, voted in favour of his appointment.
Arabs make up about 20 per cent of Israel's population, but complain of being treated like second-class citizens and of a lack of government funds for their towns and villages.
Israeli officials deny any policy of discrimination, saying Arab citizens enjoy more political freedom in Israel than anywhere in the Muslim world.
Magadla was nominated by the Labour Party for a ministerial post after one of its members quit the cabinet in protest at Lieberman's appointment in October.
The Ynet news website reported Amir Peretz, Israel's defence minister and Labour Party chief, as saying at the cabinet meeting: "I see this as a historic and important step towards equality and promoting peace in the region."
In 2001, an Israeli Druze became the first non-Jewish member of the cabinet, serving as a minister.
Several Arab politicians, however, denounced the appointment of Magadla, who replaces Ophir Pines-Paz, the former culture minister.
Mohammad Barakei, a parliamentarian from the communist Hadash Party, said: "It's not logical for an Arab minister to take the place of a Jewish minister who left the cabinet and resigned in protest against racism.
"Magadla is not an Arab minister, he is a Labour minister ... and he will sign his name to all discriminatory policies against the Arabs."
Peretz, facing an uphill battle to remain leader of the party, had pushed for the appointment of Magadla, which many see as a bid to shore up the support of Arab members ahead of a party leadership vote in May.