The measure also clears the way for employers to cite religion in determining workplace policies on dress code, grooming and bathroom and locker access.
Bryant, a Republican, said in a statement he signed the law "to protect sincerely held religious beliefs and moral convictions of individuals, organizations and private associations from discriminatory action by state government."
Mississippi is latest state drawing national protest for a law seen as anti-lesbian, gay, bisexual and transgender (LGBT). North Carolina recently barred transgender people from choosing bathrooms consistent with their gender identity.
Tennessee is considering similar legislation related to school bathrooms, and civil rights groups are watching a Missouri measure seen as discriminatory. Last week, the governors of Georgia and Virginia vetoed "religious liberty" bills.
The latest wave of measures, pushed by social conservatives, came after a U.S. Supreme Court ruling last year that legalized same-sex marriage.
The American Civil Liberties Union (ACLU) criticized the Mississippi law, which it said was set to take effect in July.
"This is a sad day for the state of Mississippi and for the thousands of Mississippians who can now be turned away from businesses, refused marriage licenses, or denied housing, essential services and needed care based on who they are," said Jennifer Riley-Collins, executive director of the ACLU of Mississippi, in a statement.
The ACLU, which is involved in a federal lawsuit challenging the North Carolina law, said it was considering its next steps in Mississippi.
The U.S. business community has pushed back against such legislation, with the North Carolina law opposed by Apple Inc, Twitter Inc, Alphabet Inc and dozens of others.
On Tuesday, PayPal Holdings Inc canceled plans to open a global operations center in Charlotte, North Carolina and invest $3.6 million locally over its new law.
In Mississippi, critics included large employers such as Nissan North America and MGM Resorts International.
Still, nearly two-thirds of Mississippi voters supported the law, according to a poll highlighted on Tuesday by the Family Research Council, an influential Christian lobbying group.
"This new law gives fresh momentum to efforts on the federal and state level to stop government discrimination against people who believe that marriage is between a man and a woman," its president, Tony Perkins, said in a statement.