The "New Light of Myanmar" says the virus was detected late last month on farms in Mayangon and Hlinethaya Townships. It says experts from the UN Food and Agriculture Organization confirmed the outbreak last week using bacteria samples from dead chickens.
The newspaper says the two poultry farms have been destroyed and sprayed with pesticide to prevent the disease from spreading.
Earlier this month, Burma confirmed additional outbreaks of the bird flu virus among poultry in the suburbs of Rangoon.
No human cases have been announced in southeast Asian country.
Bird flu is a mainly animal disease that has forced farmers to slaughter millions of birds in recent years. The disease has also killed more than 160 people since late 2003. Most of the victims came into contact with infected poultry.
Experts fear the virus could mutate into a form that is easily transmissible by human to human contact.