In a statement, the seven board members said they were "deeply troubled" by the bishops' request, and said it "undermines our moral priority of helping vulnerable children find loving homes.
"We also cannot participate in an effort to pursue legal permission to discriminate against Massachusetts citizens who want to play a part in building strong families," the statement read.
"The course the Bishops have charted threatens the very essence of our Christian mission. For the sake of the poor we serve, we pray they will reconsider."
The Vatican has said gay adoptions are "gravely immoral." On Tuesday, the state's four bishops said state law compromised their religious freedom by requiring them to consider gays as adoptive parents.
"Because of the Church's teaching, Catholic agencies may not provide adoptions to same sex couples," the bishops' statement said. "Hence we intend to seek relief from the regulatory requirements of the Commonwealth on this issue."
Gov. Mitt Romney met Wednesday with church leaders, including Boston Archbishop Sean O'Malley, and said religious institutions should be able to help people without violating their faith. But he said he had no power to waive the state's anti-discrimination laws.
"Ultimately, legislation may need to be filed to provide an exemption based on religious principles," Romney said in a statement.
In the past two decades, 13 of the 720 children placed with adoptive families by Catholic Charities have been placed in same-sex households.
Geri Denterlein, one of the board members who resigned, said she supports gay marriage, but her resignation wasn't meant as a political statement. She pointed to a unanimous vote by the 42-member board in December to continue placing children in gay households. The bishops' decision undermines Catholic Charities and eliminates same-sex couples from consideration, even if they're the best choice, Denterlein said.
"I simply didn't feel I could continue to serve as board member when we were at such odds with the way the hierarchy was approaching adoption policy," she said.
Besides Denterlein, president of Denterlein Worldwide Public Affairs, the statement was signed by Donna Gittens, chief executive officer, causemedia; Paul LaCamera, general manager, the WBUR group; Brian Leary, partner, Gadsby Hannah; Peter Meade, executive vice president, Blue Cross Blue Shield of Massachusetts; Colette Phillips, president and CEO, Colette Phillips Communications; Micho Spring, chairman, Weber Shandwick New England.
Jeff Kaneb, chairman of the Catholic Charites Board, and the Rev. J. Bryan Hehir, Catholic Charities president, released a statement saying they were "saddened" that board members felt compelled to step down.
"To lose even one of these individuals would be a severe loss to our Catholic Charities agency," the statement said. "These men and women have for many years provided Catholic Charities generously with personal commitment, professional skills and expenditure of time and financial resources."
Edward Saunders of the Massachusetts Catholic Conference, the church's public policy arm, said he had no comment on the resignations.
In 2005, Catholic Charities provided discounted fuel, food and other services to 200,000 needy people.
The agency has occasionally run up against the church hierarchy during the past few years. Last year, Boston Archbishop Sean O'Malley declined to attend the Catholic Charities Christmas fundraising dinner because it honored Mayor Thomas Menino, who supports abortion and gay marriage.
It also twice accepted funds raised by the lay reform group Voice of the Faithful, including in 2003 when interim archdiocese administrator Bishop Richard Lennon specifically instructed it to decline the money.