Quezon City local police chief Remus Medina said the shooting appeared to be the murder of the former mayor of the southern city of Lamitan, Rose Furigei.
Medina told reporters that the suspect, who was injured in a shootout with campus security and arrested after a car chase, is now in custody and being questioned.
“It looks like he was a determined killer,” Medina said, adding that two pistols were found on him.
Quezon is part of the Manila metropolitan area, spread over 16 cities and home to over 13 million people.
According to Medina, Furigei was shot dead as she was about to attend her daughter’s graduation party at the law school of Ateneo de Manila University, one of the most prestigious in the country.
The suspect, who had no relatives at graduation, was also a native of the city of Lamitan in Basilan province, a stronghold of the Abu Sayyaf, a pro-Islamist state extremist group known for its banditry and kidnappings.
The other two people killed were a campus security officer and an unidentified man, police said.
The Ateneo canceled the graduation ceremony after the shooting.
In the Southeast Asian country, shootings are sporadic and owners must have a permit to carry weapons in public. Private security guards in the Philippines carry either handguns or shotguns, and firearms are common in malls, offices, banks, restaurants, and even schools.
“We commit our law enforcement agencies to thoroughly and quickly investigate these killings and bring all those involved to justice,” said Philippine President Ferdinand Marcos Jr. says in the statement.