The missile struck the building in the town of Bilhorod-Dnistrovskyi at about 1 a.m. (2200 GMT Thursday), the ministry said in a statement. It also caused a fire in an attached store building.
Serhiy Bratchuk, spokesman for the Odesa regional administration, told Ukrainian state television that a rescue operation was under way as some people remained buried under the rubble after a section of the building collapsed.
Another missile hit a resort facility, Bratchuk said, wounding several people. Reuters could not independently confirm details of the incident.