The serviceman was detained by police but his motives remain unclear.
The incident occurred in the city of Dnipro, 500km southeast of Kyiv on Thursday morning.
The soldier, identified by the authorities as Artemiy Ryabchuk, 20, was on guard duty at a military factory and opened fire on his colleagues, fleeing the scene immediately after.
Four soldiers and one civilian died, and five more people sustained injuries.
Police detained Ryabchuk shortly after the shooting.
It was not immediately clear what prompted him to open fire.
President Volodymyr Zelenskiy demanded the authorities thoroughly investigate and analyse the incident.
"I expect law enforcement to fully inform the public about all the circumstances of the crime. Motives of the killer, how (the shooting) became possible - everything should be analysed as thoroughly as possible," Zelenskiy said in an online statement, adding that conclusions should be drawn from the incident about personnel in the National Guard.
The shooting took place against the backdrop of tensions between Russia and Ukraine.
Russia has massed an estimated 100,000 troops near its borders with Ukraine, stoking fears that such a build-up might indicate plans to invade its ex-Soviet neighbour.
The Kremlin denied harbouring such plans but demanded security guarantees from NATO, including a clause precluding the military alliance from accepting Ukraine and other former Soviet states as members - a demand the US and NATO have rejected.
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