Local police said in a statement on Friday that the deceased man had been shot in the chest, adding that he died before the ambulance arrived.
The violence in the largely Russian speaking southern port city also left dozens of people from both sides wounded.
According to police, protesters had thrown petrol bombs, paving stones and “explosive devices” during the clashes.
Tensions are also running high in other regions as Ukrainian troops continue military operations against pro-Russian protesters in the eastern regions.
According to Ukraine’s interim President Oleksandr Turchynov, many protesters have been killed on Friday during an offensive against the eastern city of Slavyansk.
The city of 180,000 residents is still under the control of pro-Russian protesters, as troops’ advance towards the city has been limited.
Earlier in the day, Kiev confirmed that pro-Russian gunmen shot down two army helicopters near Slavyansk, killing two pilots. In addition, another pilot was injured and taken to hospital by the armed men.
This is while pro-Russian protesters near the city of Yasynuvata seized a rail control center for the Donetsk region.
Over a dozen cities in eastern Ukraine are under the control of pro-Russian protesters, including Lugansk, Kramatorsk, Donetsk and Horlivka.
Pro-Russia protests gained momentum in Ukraine after Crimea declared independence from the former Soviet state and formally applied to become part of the Russian Federation following a referendum in March.