The Syrian Arab Red Crescent says its vice-president, Abdulrazak Jbeiro, has been shot dead.
The Red Crescent said he was killed as he drove from Damascus to Idlib - a focal point of the Syrian conflict. It condemned the killing.
Across Syria, 24 people were killed on Wednesday, said activists.
The Syrian army is reported to be on the second day of an offensive against insurgents in the central city of Hama.
"[Mr Jbeiro] was shot. Circumstances are still unclear," Beatrice Megevand-Roggo, head of International Committee of the Red Cross (ICRC) operations for the Near and Middle East, told Reuters news agency.
"Regardless of the circumstances, the ICRC condemns this very severely," she added.
"The lack of respect for medical services is still a great issue in Syria."
Anti-government activists the Local Co-ordination Committees (LCC) blamed his death on "security forces", while Syrian state news agency Sana pointed the finger at "a terrorist group".
Sana said the shooting occurred in the Khan Shiekoun area.
"The group opened fire with a machine-gun, hitting him in the head. He was taken to hospital where he died," Sana reported, according to news agency AFP.
As well as being vice-president, Dr Jbeiro was the head official in the northern city of Idlib.
Twenty-four Syrians died on Wednesday, the LCC said - six of them soldiers from the Free Syrian Army in clashes in Damascus suburbs.
In Homs, a woman and her five-year-old child reportedly died when a shell hit their home during clashes between troops and men believed to be defecting soldiers.
In Hama, four people died on the second day of a government bombardment, LCC said.
One of them was a Christian priest, Father Bassilius Nassar, who was helping a wounded man.
Sana said he was killed by "an armed terrorist group", according to AFP.
But LCC said the priest was "martyred" during "a military campaign conducted by the regime's forces".
The Syrian regime blames "terrorist gangs", saying they are part of an international conspiracy against Syria, for unrest that has swept the country since mid-March 2011.
The UN said in early December that more than 5,000 people had died in the Syrian unrest.
Speaking on her way into a Security Council briefing, the UN human rights chief Navi Pillay said more people had been killed since then but her office had not updated the death toll because of difficulties getting information.
"We are experiencing difficulties now because of the fragmentation on the ground," she said.
"Some areas are totally closed, such as parts of Homs, so we are unable to update that figure. But in my view 5,000 and more is a huge figure and should really shock the international community into taking action."
As the fighting in Syria continues, diplomats at the UN say European and Arab nations are meeting to try to draft a new UN resolution to address the crisis.
A previous attempt was blocked by Russia and China, and on Wednesday Russian Foreign Minister Sergei Lavrov said he was open to "constructive proposals" to end the violence.
But he reiterated his opposition to the use of force or sanctions.