Local television networks showed a visibly moved Abdel-Fattah el-Sissi visiting the woman in a Cairo hospital.
"I have come to tell you and every Egyptian woman that I am sorry. I am apologising to every Egyptian woman," said el-Sissi, a former military chief who ousted the country's first elected president nearly a year ago.
Several women were assaulted during Sunday's inaugural festivities.
The attacks were a grim reminder of one of Egyptian society's darkest sides and coincided with el-Sissi starring in carefully choreographed ceremonies held at two of the capital's most opulent presidential palaces and attended by hundreds of local and foreign dignitaries.