Villagers have been using "sticks, slingshots, and rocks" against the infestation, a local news agency said.
It is thought they have already managed to kill more than 4,000 rodents.
But while there are concerns about the disease these rats may bring to the area, locals are also worried it could herald other disasters.
"According to traditional beliefs, these animals can predict bad weather. So people here are also worried about floods or earthquakes," Regional MP Phyo Zaw Shwe told AFP news agency.
The belief may not be that far off. A study by Japanese scientists has suggested rats may be sensitive to electromagnetic waves which take place before earthquakes, according to AFP.
The rats' bodies have been sent off for testing, but so far no diseases have been found. Local officials have blamed heavy rain across the country's Ayeyarwady region for causing the infestation, which has eaten through large amounts of food.
This is not the first time a plague of rats has endangered villages in Myanmar.
In 2008, thousands of people in the north-western Chin State were left at risk of starvation after the rodents appeared and began gorging on the bamboo fruits before devouring food crops.
It is a phenomenon which happens once every 50 years. When the plague last struck in the 1950s, 15,000 people are believed to have starved to death.
Thousands of rats have descended on villages in southern Myanmar, prompting authorities to offer locals 3p (4 US cents) for every rodent they kill.