The new checkpoint policy comes at a time when Israel and the Palestinians are engaged in a new round of talks ahead of a summit expected next week in Annapolis, in the US, which is intended to restart peace negotiations.
Under the new system, UNRWA expects the annual cost of transporting and delivering aid to treble from $220,000 (£110,000) this year to $720,000 next year.
The agency provides food, clothing, education and healthcare to around 4.5 million Palestinian refugees across the Middle East.
Currently the agency's goods are checked by Israeli customs when they arrive at the Israeli port of Ashdod and are then delivered directly to the West Bank.
Negotiations between the UN and Israel on the new system are still under way. However, AbuZayd said she expected in future that all aid coming in containers from Ashdod would have to be unloaded at West Bank checkpoints and the aid packed on to pallets and reloaded into trucks on the Palestinian side - a "back-to-back" system like that in force at Gaza's commercial crossings.
At the moment the aid can pass through 12 crossing points from Israel to the West Bank, but this will be reduced to six along the West Bank barrier, the UN has been told.
"It is obvious that these new procedures will result in loss of time and an exponential increase in costs," AbuZayd said. There are already 563 obstacles in the West Bank, from permanent checkpoints to earth mounds, according to the UN.
Under the new proposals, AbuZayd said the movement of her staff would also be severely affected. UNRWA is the largest employer in the Palestinian territories, with 4,800 Palestinian staff in the West Bank and another 10,000 in Gaza.
She said there were "indications" that staff would need special permits to enter Palestinian land between the pre-1967 war Green Line and Israel's new West Bank barrier, a stretch of land known as the "seam zone".
The course of the vast concrete and steel barrier puts around 10% of the West Bank and around 50,000 Palestinians on the "Israeli" side.
The International Court of Justice advised in 2004 that the barrier was illegal where it crossed into the West Bank and should be removed.
The new checkpoint policy would also "significantly curtail" the UNRWA staff's ability to enter Jerusalem from the West Bank. It is expected to reduce the number of crossings that staff can use to enter Jerusalem from 13 to three or four.
"Unless access is assured, there will be a high human cost," said AbuZayd. "More lives will be lost, public health will suffer and the standards of education will fall. The resulting sense of isolation and abandonment accompanied by an increase in radicalism serves no one's interests."
However, Israel defended the proposed system, which it said would facilitate crossings to and from the West Bank while protecting Israel's security.
Mark Regev, a spokesman for the Israeli foreign ministry, said: "The idea of building these big crossings is to streamline the process, to make them user-friendly. The idea is to help facilitate movement and access."
He said there had been complaints of long delays at smaller checkpoints and that the larger terminals would make crossings easier. "The idea is to upgrade the system to facilitate greater efficiency," he said.
He said Israel was still cautious of security threats. "There is very clear information that the people who want to torpedo Annapolis and any renewal of talks want to upgrade their activities and this is a time when we have to be cautious," he said.