Quezon City local police chief Remus Medina said the shooting appeared to have been the assassination of the former mayor of the southern city of Lamitan, Rose Furigay.
The suspect, wounded in a shootout with a campus security officer and arrested after a car chase, was now in custody and being questioned, Medina told reporters.
“He appeared to be a determined killer,” Medina said, adding that he was found with two guns.
Quezon is part of the Manila Capital Region, an urban sprawl of 16 cities home to more than 13 million people.
Furigay was shot when she was about to attend her daughter’s graduation from the Ateneo de Manila University law school, one of the most prestigious in the country, Medina said.
The suspect, who had no relatives at the graduation, was also originally from the town of Lamitan in Basilan province, a stronghold of Abu Sayyaf, a pro-Islamist extremist group known for banditry and kidnapping.
The other two dead were a campus security officer and an unidentified man, police said.
Ateneo canceled the graduation ceremony after the shooting.
In the Southeast Asian nation, shooting incidents are sporadic, and owners require a permit to carry guns in public. Private security officers in the Philippines carry pistols or shotguns, and firearms are common in shopping malls, offices, banks, restaurants and even schools.
“We commit our law enforcement agencies to thoroughly and promptly investigate these killings and bring all those involved to justice,” Philippine President Ferdinand Marcos Jr. said in a statement.