British-Indian Kapoor "is one of the most influential and innovative artists of his generation", they said in a statement.
He won the prestigious Turner Prize in 1991 and was knighted in 2013.
"Kapoor will use this award, and the global platform provided by the Genesis Prize, to raise awareness of the plight of refugees in order to engage the Jewish community in a global effort to help alleviate the refugee crisis," it said.
The award is granted by the Israeli government, the quasi-governmental Jewish Agency and the Genesis Prize Foundation.
"It recognises individuals who have attained excellence and international renown in their fields and whose actions and achievements express a commitment to Jewish values, the Jewish community and the State of Israel," the statement said.
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Last year's winner was virtuoso Israeli-American violinist Itzhak Perlman. Other past laureates include former New York Mayor Michael Bloomberg and US actor Michael Douglas.
Kapoor, whose huge works of public art are landmarks in cities from London to Chicago, was born in Bombay, now Mumbai, in India in 1954 to a Hindu father and a Jewish mother.
"As inheritors and carriers of Jewish values it is unseemly for us to ignore the plight of people who are persecuted, who have lost everything and had to flee as refugees in mortal danger," the Genesis statement quoted him as saying.
"To lose one's home, one's land, one's sense of belonging, is bewildering. All that is left is one's body."
"Outsider consciousness resides at the heart of Jewish identity and this is what motivates me, while accepting the honour of the Genesis Prize, to re-gift the proceeds to refugee causes," Kapoor said.
Genesis said the million-dollar award has in the past been swollen by matching funds from other donors which go to laureates' projects.