Abdo Hussameddin, who took his bachelor's degree in battered Homs, announced his resignation in a video posted by activists on YouTube, saying he was joining the ranks of the rebels.
"I, the engineer Abdo Hussameddin, the deputy oil minister ... announce my defection from the regime and my resignation," he said in the video.
"I am joining the revolution of the people who reject injustice and the brutal campaign of the regime, which is seeking to crush the people's demand for freedom and dignity," he added.
The defection was welcomed by Syrian opposition leader Burhan Ghalioun, who told AFP he expects more government officials and politicians to do the same.
"I hail the deputy (oil) minister who defected and I call on all government members and public servants ... to abandon this regime and join the ranks of the revolution for freedom and dignity," said Ghalioun, head of the Syrian National Council, the main opposition group.
"I expect for sure that there are other government officials and politicians who will follow suit," he added.
Washington cautiously welcomed the news, with State Department spokeswoman Victoria Nuland saying "it would be very good news," adding that the United States could not authenticate the YouTube video
Former UN chief Annan told reporters in Cairo he had urged "the Syrian opposition to come together to work with us to find a solution that will respect the aspirations of the Syrian people."
He also warned against further militarisation of the crisis, amid a groundswell of international support for arming the rebels. The mostly army defectors who make up the Free Syrian Army are heavily outgunned by the regime forces they are battling in a number of flashpoint areas.
"I believe further militarisation will make the situation worse," Annan said after talks with Arab League Secretary General Nabil al-Arabi.
Annan, who is head to Damascus on Saturday, warned of "the possible impact of Syria on the region if there is any miscalculation."
"I hope that no one is very seriously thinking of using force in this situation," he said, adding that diplomatic efforts should be kept up.
After he spoke, Britain announced it was following the United States in considering providing "non-lethal" help to rebel groups.
"I also don't rule out giving more non-lethal help, but we haven't countenanced doing that beyond groups that are, so far, located outside Syria and are trying to pursue a peaceful, democratic transition," Foreign Secretary William Hague told members of the parliamentary Foreign Affairs Committee.
Late on Wednesday, US Defence Secretary Leon Panetta said Washington was looking at delivering non-lethal aid to Syria's rebels, hinting at the first direct US assistance to the forces seeking Assad's downfall.
Asked if the United States was ready to deliver communications equipment to Syrian rebels, Panetta told the Senate Armed Services Committee: "I'd prefer to discuss that in a closed session but I can tell you that we're considering an array of non-lethal assistance."
In Idlib province in the northwest, the Syrian army pressed a troop buildup that the Syrian Observatory said appeared to indicate a major assault was imminent.
Tanks and troops were deploying heavily around the province's Jabal al-Zawiya district near the border with Turkey, where rebel fighters have been active, Milad Fadl, a member of the opposition Syrian Revolution General Commission, said.
"Large numbers of residents from eight villages in that area have fled," Fadl told AFP, adding that people were also leaving the city of Idlib itself.
He said one civilian was "executed" on Thursday in Jabal al-Zawiya and five homes were burned down to punish the local population for supporting the rebel fighters.
State news agency SANA said "armed terrorist gangs" were looting and destroying property in several towns and villages in the province.
Two civilians also died in clashes in the town of Al-Mayadin, in the eastern province of Deir Ezzor, and another in Daraya village, in Damascus province, the Observatory said.
Two more civilians were killed at a checkpoint in Homs province, where a top human rights lawyer, Omar Qandarji, was detained as he went to visit his mother in the battered neighbourhood of Inshaat, the Britain-based watchdog added.