All those infected with the virus have been hospitalized, the Interfax news agency said, citing officials from the Emergency Situations Ministry.
The number of infected patients reported is unclear -- while the news agency said 136 people had caught the virus, including 61 children, a top public health official said Tuesday that 90 were still being treated for the disease and indicated that the worst was over.
Dr. Gennady Onishenko, Russia's senior public health official, said the unknown viral infection had been diagnosed as Congo-Crimean Hemorrhagic Fever.
"We can say the peak seems to have already been reached. It is under control," he told Reuters.
Characterized by fever, chills, headache, breathing and digestive problems, hemorrhagic fever can lead to bleeding from tiny blood vessels and to kidney failure.
Onishenko said the disease "belongs to a type of low-contagious infection," and can be picked up from ticks and household animals which do not show any symptoms of the disease.
It has appeared previously in Russia, the Middle East and Africa, causing death in between two and 50 percent of those infected. In its worst form it causes the patient to bleed to death through the nose, eyes, uterus or other mucous membranes.
The lurid symptoms caused a fever of speculation about the disease in the Russian press. Tuesday's edition of Komsomolskaya Pravda, a popular tabloid, featured a cover photo of a child, barely conscious, with a tube in his mouth.
"First the rumors. They said the village of Oblivskaya was punished by God. They said that Chechens had poisoned the water supply...People panicked," its correspondent wrote.
Russia's RTR television said rumors had spread that vodka and garlic prevented the disease, and "there is now a shortage of these products" in the Rostov region.
The disease has an incubation period of about three to 12 days, which means doctors can determine fairly reliably when an outbreak has subsided if no new cases appear among family members of those infected, Wright
Local authorities are not planning to introduce a quarantine in Rostov, Onishenko said.