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The International Testing Agency (ITA) said on Thursday that a sample taken on 14 February had contained dehydrochloromethyl-testosterone.
Hunko, 28, has been provisionally suspended.
It is the third positive test at the Games and the second by a Ukrainian after cross-country skier Valentyna Kaminska.
Iranian skier Saveh Shemshaki was the first athlete to return a positive doping test last week.
The second week of the Winter Olympics has been dominated by the case of Kamila Valieva.
The 15-year-old Russian figure skater was allowed to compete in Beijing despite testing positive for banned angina drug trimetazidine before the Games.
Her controversial Winter Olympics ended in tears on Thursday with a fourth-place finish in the women's event after she fell multiple times in the free skate.
