One of the suspects, who was being driven to a military training centre on Friday with other conscripts, called an acquaintance who then arrived at the scene and shot dead one of the accompanying officers, the Prosecutor General's office said.
The two men fled but were arrested a few hours later, the office said in a statement, adding that police had seized a hunting rifle, ammunition and two cases of hand grenades from the alleged shooter.
One suspect was charged with obstructing the military and murder, and the other with aiding and abetting military obstruction.
Ukraine's war mobilisation campaign has been in the spotlight as military analysts and foreign officials describe Ukraine's manpower shortage at the front as a key battlefield weakness.
The call-up effort has been marked by faltering enthusiasm for service amid reports of draft-office corruption, poor training and instances of weak battlefield command amid reports of attacks on draft officers or recruiting centres.
Mykhailo Drapatyi, the commander of Ukraine's ground forces, condemned the draft officer's killing on Sunday, describing it as "a red line that cannot be crossed" and calling for the perpetrators to be swiftly punished.
"We have no right to silently observe the growing wave of contempt toward defenders of Ukraine," Drapatyi said in a statement on social media.
Ukrainian President Volodymyr Zelenskiy urged allies to provide more support on Sunday, saying more than 1400 Russian air strikes had targeted his country in the past week.
"Every day, Russia attacks Ukraine with drones, missiles and aerial bombs," he said on Telegram.
Accompanying his statement was a video showing images of death and destruction in Ukrainian cities.
Russia attacked Ukraine with about 50 missiles, nearly 660 drones and more than 760 glide bombs in the past week, he said.
"Russia will not stop on its own. The world must force it to end this brutal and unprovoked aggression," Zelenskiy said.
"Strengthening our defence is absolutely necessary. We need better protection - air defence systems, long-range weapons and sanctions pressure," he said.
According to Ukrainian authorities, 15 historical buildings in the centre of the port city of Odessa, a UNESCO World Heritage Site, were damaged in Russian rocket attacks.
Ukraine has been defending itself against Russia's full-scale invasion for almost three years.
with DPA
