The country's central and southern parts are reported to be the most affected.
So far, the remains of 14 people have been found in the Jablanica region, about 70 kilometers southwest of Sarajevo, says the region's spokesperson Darko Jukan.
According to Jukan, it is likely that the number of dead will rise. The Jablanica region appears to be the most affected at present, the town of the same name with 4,000 inhabitants is completely cut off from the outside world, according to the rescue service.
A number of people in the area have been reported missing and helicopters have been deployed to evacuate the injured.
In Kiseljak, two miles west of Sarajevo, houses, gardens, and cars are underwater after the rain, which has lasted for over 24 hours.
The fire department and police have been deployed in the rescue efforts, but more help will be needed, warn federal authorities.