Officials said several other people, including children, might be trapped under tons of rubble.
The Emergency Situations Ministry said in a statement that rescuers had retrieved one body from the building in the Black Sea port city.
Most Ukrainian homes use natural gas for cooking and heating, and leaks are frequent in aging apartments and houses, killing and injuring scores of people each year.
RFE/RL's World: 2005 In Pictures
A slideshow of images related to the top news stories of 2005 from throughout RFE/RL's broadcast region with links to RFE/RL's reporting.