Georgette Mulheir has been chief executive of the charity since 2011.
The author set up the foundation in 2005 and donates some royalties to it to help children in orphanages and similar institutions around the world.
The charity will now set up independent reviews of its governance and culture.
According to The Times, some former staff members have complained of a culture of “borderline bullying” and nepotism. A spokeswoman for the charity told the BBC in a statement: “The board takes allegations of this nature seriously. “We were founded to help the most vulnerable people in society and we hold true to our principle of fair treatment for everyone today. That’s why we have commissioned independent reviews into the charity’s governance and culture. All necessary steps will be taken in response to any findings to ensure this is an organisation where everyone feels respected and valued.”
Announcing Ms Mulheir’s departure, Rowling’s agent and Lumos chairman Neil Blair said: “Recently the board of trustees has identified some management and culture challenges facing Lumos that require immediate action.”