"The government of Israel today mourns the death of our dear friend, the late minister David Azoulay," Netanyahu wrote in Hebrew on Twitter.
"For a long time we prayed for David's recovery, as he was fighting a serious illness," he said. "Unfortunately, his struggle for life ended a few hours ago." The cabinet office said that he would be buried in Jerusalem at 11:00 pm (2100 GMT).
Jewish custom demands burial as soon as possible after death.
The 64-year-old's death was announced on Facebook by his ultra-Orthodox Shas party, which said it "bows its head" at his passing.
Writing on the same online page, Interior Minister Arye Deri wrote: "I weep for my dear and beloved friend and my comrade of many years." Azoulay was born in January 1954 in Morocco and emigrated with his family to Israel in 1963, according to his official parliamentary biography.
A former schoolteacher, he was first elected to parliament in 1996 and was appointed to Netanyahu's cabinet in 2015.
Haaretz newspaper said that in recent years he had battled cancer and recently relinquished his seat in parliament as his condition worsened.
He is survived by a wife and four children, it said.
Azoulay drew fire from US Jews in July 2015 after he said in a radio interview that he "could not say" that members of the Reform movement were fully Jewish.
"These are Jews that have lost their way," he added.
Israeli President Reuven Rivlin described Azoulay as a man "who faithfully dealt with the needs of the public his whole life".
"Recently, he dealt bravely with his illness but made sure to serve the public as far as he could," Rivlin wrote in a statement.
(With inputs from agencies.)