Most of the victims were in and around the city of Timisoara, where winds of up to 100km/h (60mph) brought down trees and tore off roofs.
Some water and electricity supplies have been cut.
"We weren't warned about this. The weather report only called for rain," Timisoara's mayor Nicolae Robu told TV channel Digi 24.
Romania's emergency services urged people to shelter indoors and avoid going near trees or power lines.
The storm is currently moving north towards Ukraine.
Photo caption: The storm brought down trees, damaging cars