More than 80,000 school-aged Syrian children in the kingdom received no formal education in the last school year, it said.
In a 97-page report entitled: "We’re Afraid For Their Future", the rights organisation said a series of obstacles are preventing Syrian children from going to school.
It said many were barred from public schools for lack of "service cards" issued to Syrians living outside formal refugee camps.
HRW estimated that "tens of thousands" of Syrians are ineligible for the cards due to lack of paperwork or failing to meet stringent criteria.
Jordanian regulations also bar children from entering school if they have been out of education for three or more years, the group said.
It said poverty was a "major driver" of drop-outs. Some families can barely afford transport costs, and many children are pressured to work in the informal sector.
Children are at lower risk than adults of being arrested for working without hard-to-obtain work permits, meaning many work long hours in hazardous conditions that violate Jordanian labour laws, it said.
Jordan says it is hosting nearly 1.4 million refugees, of whom 630,000 are registered with the United Nations.
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HRW praised Jordan's "generous efforts" to enrol Syrians in its public schools, which were already struggling with capacity and quality issues before the influx of refugees.
Jordan opened schools in refugee camps and put in place a "double shift" system to give more school places to Syrians.
But over a third of the 226,000 school-aged Syrians registered with the UN refugee agency in Jordan received no formal education in the last school year, HRW said.
"Authorities should expand efforts to realise the fundamental right to education for all Syrian children," it said.
Jordan frequently says it is not receiving enough international support to help it cope with the hundreds of thousands of Syrians it is hosting.
King Abdullah II said on Monday that donations from the international community only covered 35 percent of the cost of hosting the refugees, leaving Jordan to make up the shortfall.
That took up more than a quarter of Jordan's budget, he said in an interview with the semi-governmental Addustour newspaper.
"Jordan is doing its utmost to help refugees," he said.
"However, we have reached our limits... This is an international crisis and an international responsibility, and the world has to do its part."