The move comes with the UN and the European Union raising concern over a sharp increase in demolitions by Israel in recent weeks.
Many of the structures targeted have been financed by the international community.
The Bedouin school, which was demolished early Sunday before it could be used, was funded by France.
The 25 students aged between seven and eight held their Arabic and English classes on Wednesday while seated on the ground in the area where pre-fabricated buildings previously stood.
School director Asma Sheha said that the Israeli military had also taken away benches and tables. On Tuesday, children ran for shelter as it began to rain.
The Bedouin community, Abu Nawwar, is located in a sensitive area of the occupied West Bank seen as key to any future settlement of the Israeli-Palestinian conflict.
The European Union expressed "deep concern at an unprecedented number of demolitions and confiscations of Palestinian structures" in the part of the West Bank under complete Israeli control.
"These include the dismantlement and confiscation of the school in Abu Nawwar on 21st February, which was funded by France and is the only school in a Bedouin community severely threatened in its existence," it said in a statement.
France also condemned the demolition of the school, installed last week.
Israel says such demolitions occur because the structures have not been granted permits.
Asked about the school, the Israeli defence ministry unit in charge of civilian affairs in the West Bank, known as COGAT, said it had removed four pre-fabricated buildings that had been illegally installed.
Palestinians and their supporters say it is extremely difficult for them to obtain permits in areas of the West Bank under full Israeli control, known as Area C and which accounts for about 60 percent of the territory.
Nickolay Mladenov, UN special coordinator for the Middle East peace process, said last week that the number of such demolitions had tripled on average since the start of the year.
"During the past few weeks alone, Israeli authorities in Area C and east Jerusalem demolished 201 Palestinian-owned structures, including 79 which were donor-funded," he said in a briefing to the UN Security Council.
"As a result, 320 people were displaced. Since the beginning of 2016, Israel has demolished, on average, 29 Palestinian-owned structures per week, three times the weekly average for 2015. These actions run directly counter to the idea of peace."