UNRWA's decision came hours after the Israeli army said it shut two key crossings with Gaza through which most of the Hamas-ruled territory is supplied after its troops came under mortar fire.
The Karni and Nahal Oz crossings, through which most of the impoverished territory receives its food, medical supplies, humanitarian aid and fuel, would remain closed "until further notice," an army spokeswoman said.
Mike Hanna, Al Jazeera's correspondent in Gaza, said: "Certainly its a very dire situation indeed. Seen in a wider context, this is just one issue that is plaguing Gazans every single day."
Cars in Gaza, lacking fuel, have largely begun using a mixture of petrol and cooking oil in its place.
Hanna said: "The dangers of this are obviously its going to shorten the life of the engines, but also, these are time bombs on the road. At any stage, one of them could explode, creating great loss of life.
"In the wider scheme of things, the situation in Gaza is absolutely desperate. This is a humanitarian crisis."
The Jewish state previously closed down the Nahal Oz crossing and fuel terminal after two Israeli civilians were killed in an attack, causing an acute shortage of fuel in Gaza.
Israel imposed a punishing blockade on the Gaza Strip after the Hamas movement seized power in the territory nearly a year ago, allowing only a minimum of basic supplies through the crossings.
It says it will only consider easing the blockade if there is a complete end to cross-border attacks by Palestinian armed groups.
However, in Cairo last month, 12 Palestinian factions, including Hamas, agreed to observe a six month ceasefire, on condition that Israel end the blockade and stop its cross-border raids.
Hanna said: "Effectively each side is insistent that improving the situation in Gaza is dependent on action by the other, a fundamental disagreement about what should come first."