Kapoor, 62, spoke out against "abhorrent government policies" towards refugees as he was named the recipient of this year's Genesis prize, dubbed Jewish Nobel.
The prize committee, headed by Jewish Agency Chairman Natan Sharansky, acknowledged Kapoor as "one of the most influential and innovative artists of his generation".
Kapoor joins Itzhak Perlman, former New York City Mayor Michael Bloomberg, and actor-director Michael Douglas as recipients.
Kapoor, born in Mumbai to an Iraqi-origin Jewish mother and Indian father, said he will donate the award money to help people who have fled war or persecution.
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More than 12.5 million Syrians, including 2.5 million children, have been displaced during the current political turmoil in the West Asian state, he noted.
"Jewish identity and history have witnessed recurring conditions of indifference, persecution and Holocaust. Repeatedly, we have had to repossess ourselves and re-identify our communities," Kapoor said.
"As inheritors and carriers of Jewish values, it is unseemly, therefore, for us to ignore the plight of people who are persecuted, who have lost everything and had to flee as refugees in mortal danger," he said.
He also made a passionate plea to Jews around the world to speak out for refugees wherever they are.
"I am an artist, not a politician, and I feel I must speak out against indifference for the suffering of others. There are over 60 million refugees in the world today - whatever the geography of displacement, the refugees crisis is right here on our doorstep," he said.
Kapoor created the Holocaust Memorial for the Liberal Jewish Synagogue in London and the 70 candles for Holocaust Memorial Day in Britain in 2015, commemorating the 70th anniversary of the liberation of Auschwitz from the Nazis.
Sharansky, who heads the prize committee, said, "Throughout our history, the Jewish people suffered not only from active and violent antisemitism, perpetrated by a minority, but also from the indifference of the majority."
"It is this indifference that made persecution, massacres and the Holocaust possible. Anish Kapoor has campaigned against this. His message is clear, powerful and inspiring," he added.
Stan Polovets, chairman and co-founder of the Genesis Prize Foundation, said the profound impact of Kapoor's work continues a long history of Jewish contribution to the arts, while his social activism reaffirms the commitment of the Jewish people to humanitarian causes.