President Liz Thompson will leave Komen next month and Brinker will relinquish her chief executive's role for one more focused on fundraising and strategic planning, the Dallas-based organization said.
It's the latest shakeup since news emerged in January that Komen had decided to eliminate its funding for Planned Parenthood for breast-cancer screening. After a three-day firestorm, Komen reversed restored the funding -- though that didn't quell the criticism.
At least five other high-ranking executives have resigned in recent months.
Brinker founded the organization in 1982, two years after her sister, Susan G. Komen, died of breast cancer. Thompson joined the group in 2008 to head research and scientific programs, and she was promoted to president in 2010.
According to the statement, Thompson said the time was right for her to pursue other opportunities. She hailed the organization's leadership in pursuing a cure for breast cancer and for helping women and men with cancer screening, diagnosis and treatment.
"That legacy will continue. It has been a privilege and an honor to serve in this role," she said.
Brinker praised Thompson's work in expanding Komen's influence in scientific, community health, advocacy and global programs. As for her changed role, Brinker said she assumed the chief executive's duties at the request of the foundation's board in 2009.
"Three years into that role, and 32 years after my promise to my sister to end breast cancer, I want now to focus on Susan G. Komen's global mission and raising resources to bring our promise to women all around the world," she said.
Cecile Richards, president of Planned Parenthood Federation of America, praised both women for their "profound contributions to women's health" and for helping elevate the importance of breast cancer detection and prevention.
She also noted that "the Komen-funded Planned Parenthood programs have helped thousands of women in rural and underserved communities get breast health education, screenings, and referrals for mammograms. We are proud to continue this work together."
Some Komen affiliates were among those publicly opposed to cutting off Planned Parenthood. Komen said it had decided to withhold the funds because Planned Parenthood was the focus of a congressional investigation launched at the urging of anti-abortion activists.
In the days after the organization reversed that decision, Komen policy chief Karen Handel resigned. She had opposed abortion as a Republican candidate for Georgia governor and had become a target of those angry about the decision to halt funding to Planned Parenthood.
Her resignation was followed, in quick succession, by Katrina McGhee, executive vice president and chief marketing officer; Nancy Macgregor, vice president of global networks; and Joanna Newcomb, director of affiliate strategy and planning.
And organizers of individual Race for the Cure events -- 5K runs and walks that account for most of the charity's fundraising -- saw participation decline by as much as 30 percent. Most also saw their fundraising numbers sink, although a couple of races brought in more money.
Race organizers acknowledge the effect of the Planned Parenthood debacle, which angered people on both sides of the abortion debate.
According to Komen's statement Wednesday, the foundation has invested $1.3 billion in community programs over 30 years to pay for screenings, education and financial and psychological support for those fighting breast cancer.
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