The group is being held by armed fighters near the Golan Heights.
They had been monitoring the ceasefire line between Syria and Israel, which captured the Heights in 1967.
The Philippines foreign affairs ministry said the observers were being treated well and that negotiations were under way to secure their release.
“The main concern of the Philippine government at this time is to ensure the safety and well-being of our peacekeepers,” said Foreign Affairs Secretary Albert del Rosario, insisting that the UN mission must be respected.
Army spokesman Colonel Arnulfo Burgos told AFP: “We have high hopes that they are going to be released soon.”
The UN says the peacekeepers from the United Nations Disengagement Observer Force (Undof) were on “a regular supply mission” on Thursday when they were stopped near an observation post by the armed men.
UN deputy spokesman Eduardo del Buey said the post had sustained damage and was evacuated over the past weekend following “heavy combat in close proximity”.
The spokesman did not provide any further details.
A video posted on the internet showed men claiming to be Syrian rebels standing next to vehicles with the letters “UN” written on them.
They identify themselves as the “Martyrs of Yarmouk” and are heard saying that the UN personnel would not be released until forces loyal to Syrian President Bashar al-Assad withdrew from the village of Jamla in the area.
The rebels later said they had taken monitors to try to stop the Syrian army from firing on them and civilians in the areas, and said they were being treated as guests.
The video was circulated by the UK-based Syrian Observatory for Human Rights (SOHR).
The SOHR is one of the most prominent organisations documenting and reporting incidents and casualties in the Syrian conflict. The group says its reports are impartial, though its information cannot be independently verified.
The Free Syrian Army (FSA) – the main rebel fighting force – condemned the seizure of the UN observers.
FSA leader Gen Salim Idriss told the BBC’s Newshour programme he would do everything he could to to free them.
UN Secretary General Ban Ki-moon also condemned the detention of the observers and demanded their immediate release, as did Russia’s UN ambassador Vitaly Churkin, who currently holds the presidency of the UN Security Council.
In a separate development, the New York-based pressure group Human Rights Watch said it was investigating whether the same rebels were involved in the executions of seized Syrian government soldiers earlier this month.
The UN has had its monitors in the area since the 1974 ceasefire between Israel and Syria.
Israel has occupied the Golan Heights since 1967 and later annexed the territory – in a move that is not internationally recognised.
Recently there has been fighting in the eastern foothills of the Golan Heights between Syrian President Bashar al-Assad’s forces and rebels.
Israel has said its policy is not to get involved in the Syrian conflict. However, in recent months it has retaliated when there has been Syrian fire into Israeli-controlled areas.
Israel has also reinforced a fence that runs along the armistice line, and officials say Syrian refugees will not be allowed into Israel en masse.
Up to 70,000 people have been killed and a million refugees have fled since the crisis in Syria began two years ago.