"The slaughtering and incineration of the pigs will begin Monday," the head of the local veterinary authority Gicu Dragan told AFP.
The outbreak was discovered last week and confirmed by the Institute for Veterinary Diagnosis and Animal Health, Dragan said.
The pigs are partly wild and come from private farms located around the uninhabited park near Braila, he added.
Some 50,000 pigs were already slaughtered in August in three farms in western Timis county belonging to the US company Smithfield, after swine fever was discovered there.
Romanian authorities had announced in June that they had eradicated the last case of the disease, after discovering 716 outbreaks around the country in 2006.
Following the most recent cases, Brussels decided last month to extend its embargo on Romanian pork until the end of 2009.