Drew Gilpin Faust, a historian specialising in the US civil war, was named 28th president of the oldest US institute of higher learning on Sunday.
"I'm not the woman president of Harvard. I'm the president of Harvard and I was chosen as the president of Harvard," she said.
Summers created an uproar in 2005 when he said that genetic gender differences may explain why few women rise to the highest science jobs.
Last Mod: 20 Eylül 2018, 18:16
He later apologised for his remarks.
He was also embroiled in a public feud with the African-American Studies department that erupted shortly after he became president in 2001.
Faust also becomes the first president without a Harvard degree since Charles Chauncy, who graduated from Cambridge University, died in office in 1672.
She attended Bryn Mawr College and the University of Pennsylvania, where she was also a professor of Southern history.
The Harvard presidency is one of the most prestigious jobs in US higher education and the university has a budget of $30bn.