The Philippine Star reported gunmen on motorcycles fired at the victims as they stepped out from the arrival area and then fled.
Jose Angel Honrado, manager of the Philippine capital's airport, said those killed included Ukol Talumpa, mayor of the town of Labangan in Zamboanga del Sur province, ABS-CBN reported.
The ABS-CBN report said the mayor's wife, Lea, and their nephew, Salipudin Talumpa, 25, also died in the shootings. The baby who died was the child of a bystander, officials said.
The gunmen escaped, the New York Times reported.
Honrado said Talumpa and his relatives arrived at the airport from their home province. He said investigators had obtained a mobile phone video that had captured the shootings.
A police official was quoted as saying the gunmen were in police uniforms.
Leila de Lima, Secretary of the Department of Justice, said there had been two previous attempts to kill Talumpa.
The New York Times added his home province is an area where political violence is common.
"We are still investigating the motive, "Honrado said.