Bogdanovic, 60, allegedly shot and killed six men, six women and a 2-year-old boy in the village of Velika Ivanca, about 30 miles south of Belgrade, before shooting his wife and then trying to take his own life.
He died from massive head wounds, the report said.
The suspect's wife, Javorka Bogdanovic, 60, was reported in stable condition after undergoing surgery Wednesday.
Investigators have not determined a motive for the massacre.
Funerals are to be held Friday in Velika Ivanca for all 13 of Ljubisa Bogdanovic's alleged victims.
A day of mourning was declared in Serbia Wednesday and the government ordered flags flown at half-staff at state buildings and sports and cultural events.