Cook, who publicly declared his sexual orientation last year, joined other tech chief executives, including Salesforce.com Inc's Marc Benioff, in blasting the Religious Freedom Restoration Act, which could let business and individuals turn away customers by citing "religious freedom."
Indiana Governor Mike Pence signed the controversial bill into law.
"Apple is open for everyone. We are deeply disappointed in Indiana's new law," Cook tweeted to his one million-plus followers. "Around the world, we strive to treat every customer the same - regardless of where they come from, how they worship or who they love."
Legal experts say the act sets a legal standard that will allow people of all faiths to bring religious freedom claims, but opinions differ over its impact.
Supporters of the bill, which was passed overwhelmingly by both chambers of the Republican-controlled state legislature, say it will keep the government from forcing business owners to act against strongly held religious beliefs.
Opponents say it is discriminatory and broader than other state religious freedom laws. Gay rights groups worry it will be used by businesses that do not want to provide services for same-sex weddings. Gay marriage became legal in Indiana last year, following an appeals court ruling.
Other tech chief executive officers have also spoken out against the bill. Benioff said on Twitter that his San Francisco-based company would cancel programs that require travel to Indiana. And Yelp Inc chief executive officer Jeremy Stoppelman wrote an open letter criticising discrimination laws. — Reuters