A former mayor, Rose Furigay, is among the dead. She was attending the graduation of her daughter, who was injured in the shooting in Quezon City.
The alleged gunman has been arrested. He is thought to have been involved in a legal dispute with Furigay.
School and university shootings are rare in the Philippines but killings of politicians are fairly common.
The shooting happened at Ateneo de Manila University, during an event for law students and their families.
Furigay was mayor of Lamitan, a city in the Philippines’ restive south. But police pointed to the suspect’s “long history” of disputes with Furigay.
Her assistant and one of the university’s security guards were also killed during the attack.
Police have said Furigay’s daughter was in a stable condition in hospital.
Alexander Gesmundo, chief justice of the Philippines, was on his way to speak at the ceremony moments before the shooting.
In a statement, Philippines President Ferdinand Marcos Jr said police would “thoroughly and swiftly investigate these killings and bring all involved to justice”.
