Ban said 15-year-old Malala Yousufzai was the "global symbol" of every girl's right to an education, The News International reported.
The secretary-general said 61 million children around the globe do not go to school.
In a video message posted on the U.N. website, Ban said, "Education is a fundamental human right. It is a pathway to development, tolerance and global citizenship."
During a ceremony in Islamabad, Gordon Brown, the U.N.'s special envoy for global education, presented President Asif Ali Zardari with a petition signed by more than 1 million people in support of Malala.
Zardari also signed the petition.
Brown said the day was aimed at creating awareness of the right of 32 million girls in Pakistan to an education, The Nation reported.
A British-Pakistani girl, Shahida Chaudhry, has begun a petition campaign for Malala to receive the Nobel Peace Prize.
"Malala doesn't just represent one young woman, she speaks out for all those who are denied an education purely on the basis of their gender," Chaudhry said.