Asbar headed the Syrian Scientific Research Centre in Masyaf, Hama province, which the United States claimed was developing sarin gas used by the Syrian regime.
The pro-regime Al Watan newspaper confirmed the killing.
The pro-government Al Watan newspaper reported on its website that Aziz Esber, of the Scientific Studies and Research Centre, died in a blast targeting his auto in Hama province.
"[Asber] died after an explosion targeted his auto in the Hama countryside", it said.
There have been no official comments from the Syrian government, with pro-government activists posting photos online of a charred vehicle said to be the scientist's.
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The unit was said to be developing short-range surface-to-surface missiles with experts present from the Syrian regime's ally, Iran.
The center has been targeted in two air attacks that have been attributed to Israel, including one in April that killed several Iranians.
Israel is believed to be behind air strikes targeting the centre's facilities in Masyaf last month and last September.
An Israeli government official declined to comment on reports of Asber's death when asked by the Reuters news agency. Esber was not on the list of targeted individuals.
The US and its allies also blamed government forces for a sarin attack on the suburbs of Damascus in 2013 that killed around 1,000 people.