"Syria has already received more than 1.5 million refugees and there could be no end in sight to what the Americans unleashed there. We simply can't cope any more," a Syrian official said.
The UN estimates that 30,000 Iraqi refugees enter Syria every month.
Jordan, the other main goal of Iraqi refugees, imposed its own visa requirements two years ago.
Diplomats said Syrian officials informed Nuri al-Maliki of their intension to stop the influx during a visit by the Iraqi prime minister to Damascus last month.
The Iraqi foreign ministry said on its website that Syria has asked for Iraqi co-operation to implement the new visa system.
Iraqis could previously turn up at any Syrian border point and be automatically issued a three-month visa.
Under the new government decree, visas can be issued only to businessmen and academics by Syrian embassies abroad.
Iraqi fears
In Damascus, the Syrian capital, Iraqis expressed frustration at the new regulations.
"All the roads in front of us are now blocked. Arab governments are making the lives of Iraqis even more miserable," said Fadel Ahmad, who came from Baghdad.
Wafa Mahdi, a former school teacher, said: "Escaping to Syria has kept me and my family alive. What are people facing death and eviction from there homes in Iraq supposed to do now?"
Following an Arab nationalist policy, Syria does not normally impose visa requirements on the citizens of other Arab states.
On Thursday, the UNHCR appealed for greater help for both Syria and Jordan to cope with the refugee influx.
"The international community has a big debt of gratitude towards these two countries" whose limited resources have been stretched, said Antonio Guterres, the UN high commissioner for refugees, in Vienna.