Burke submitted his resignation as chairman of the board for the Cardinal Glennon Children's Foundation, saying the decision to let Crow sing on Saturday left him no other choice.
"It's very painful for me," Burke said during a news conference Wednesday. "But I have to answer to God for the responsibility I have as archbishop.
"A Catholic institution featuring a performer who promotes moral evil gives the impression that the church is somehow inconsistent in its teaching," Burke said.
Crow is set to appear at the 19th annual benefit for the Bob Costas Cancer Center at Cardinal Glennon Children's Medical Center. Costas will host the event, which will also feature comedian Billy Crystal.
Event organizer Allen Allred said he was disappointed with Burke's decision, but that Crow would appear as scheduled.
"This is not an event that's about ideology," Allred said. "This is about helping kids."
Burke made national news during the 2004 U.S. presidential campaign, by saying he would deny Communion to Democratic presidential nominee John Kerry, a Catholic who supports abortion rights.
He later clarified the statement to say Catholics can vote for such candidates if they believe the candidate's stance on other moral issues outweighs the abortion-rights stance.
Burke said it was a "scandal" to let Crow sing at the event and amounted to an act that could lead others to evil. He cited Crow's support for stem cell research and "procured abortion."
Burke said he became aware of Crow's participation in the cancer benefit in February and asked other board members to cancel her appearance.
"They didn't accept my concerns," Burke said.
Allred said board members did not honor Burke's request because they did not want to play politics with performers at the annual event.
Costas, a prominent TV sportscaster, released a statement supporting the board's decision.
"I have never applied a litmus test, Catholic or otherwise, concerning the politics or religious beliefs of any of the generous performers who have come to St. Louis to help this worthy cause, nor do I intend to ..." Costas wrote
Criticism of the Catholic foundation is reminiscent of some earlier statements by Burke, who has been outspoken in his public condemnations of Roman Catholics who dissent from church teaching.
Crow appeared in television ads throughout Missouri last year asking voters to approve an initiative that enshrined the right to conduct stem cell research in the state constitution.
Crow's publicist did not return a message seeking comment Wednesday.