The XiamenAir aircraft overshot shortly before midnight local time (GMT+7) on Thursday (August 16) forcing airport officials to close the main runway at Ninoy Aquino International.
No one was hurt, with all 157 passengers and eight crew safely escaping the stricken aircraft via the escape chutes.
A joint investigation involving the Manila International Airport Authority and Philippine Civil Aviation Authority is under way.
The runway was expected to be shut until around midday on Friday local time (5am GMT).
However, efforts to recover the aircraft were ongoing into the afternoon.
Images from the scene posted to social media by the AFP news agency show the aircraft having come to a halt on the grassy run off beside the runway, missing its portside engine.
A XiamenAir Boeing 737-800 series passenger aircraft, operating as flight MF8667 from Xiamen to Manila, skidded off the runway while attempting to land in bad weather at the Manila international airport. \uD83D\uDCF7 by AFP's Ted Aljibe pic.twitter.com/65dixsiqUu— AFP news agency (@AFP) August 17, 2018
In a statement, the airport authority said: “On or about 11.55pm on August 16, XiamenAir flight MF8667 went off the runway during [a] heavy downpour. All 157 passengers and flight crew are safe.
“Investigators are already on site to determine the cause of the accident. Passengers were evacuated using the aircraft’s emergency chute.”
In its own statement, the airline added: “The [Boeing 737-800] aircraft skidded off the runway while landing at Manila international airport. The specific cause of the incident is still under investigation.” All 157 passengers and eight crew members were evacuated safely and no one was hurt.”
Dozens of flights have been cancelled or diverted, primarily affecting airlines serving south east Asia, the Middle East and North America.
The Foreign Office has also updated its advice for any Britons travelling to Manila.
"Ninoy Aquino International Airport (NAIA) in Manila is experiencing flight disruption due to an incident late on August 16," said the FCO.
"You should check with your airline if you’re due to travel; NAIA flight information is available on their Hotline +63 (0) 2877 1111."