The underwater quakes struck at a depth of between 575 and 605 kilometres, just over 100 kilometres southwest of Cotabato, on the island of Mindanao, said the US Geological Survey.
The Hawaii-based Pacific Tsunami Warning Centre said no destructive tsunami was generated by the 7.3-, 7.6- and 7.4-magnitude quakes, the first of which hit at 6:08 am (0338 IST).
"It was kind of mild," said Monisa Tulawie, a staff member at the Cotabato city mayor's office, who told AFP she felt one of the quakes.
Other residents contacted by phone were unaware of what had happened, saying they had not been woken by the tremors.
"We have received no reports of damage or casualties," said local fire official Marlon Macapili of the Autonomous Region in Muslim Mindanao, a self-ruled area that includes four provinces around Cotabato.
Renato Solidum, chief of the Philippine Institute of Volcanology and Seismology, said the strong quakes struck over a 67-minute period at sunrise, with several moderate aftershocks.
Mild tremors were felt as far as north Manila, more than 800 kilometres away, he added.
"We don't expect any," Solidum told AFP when asked about damage or casualties. "Because of their depth they will not be able to depress the ocean floor," Solidum added.
The institute said quakes with a magnitude of 7.0 or above can cause considerable damage near their epicentre, while shallow-seated ones occurring under the sea may generate huge waves.
The Philippines is an archipelago of more than 7,000 islands with many people living in communities close to the sea.
The country sits on the Pacific Ring of Fire, where continental plates meet, causing frequent seismic and volcanic activity.
Solidum said a movement of the Molucca Sea Plate had caused today's quakes. The plate is pushing underneath the Indonesian archipelago.