Tremors were felt as far away as Bangkok, almost 800 kilometres (500 miles) from the epicentre, Hanoi and parts of China during the earthquake yesterday, which the US Geological Survey (USGS) measured at magnitude 6.8.
A Myanmar official said dozens of people were killed in areas close to the epicentre and more than 240 buildings had collapsed.
"The death toll has increased to more than 60 now from those areas including Tarlay, Mine Lin and Tachileik townships," said the official.
"About 90 people were injured from those areas. The officials are still trying to reach some more affected areas.
There are some places we cannot reach yet." Across the border, Thai authorities said a 52-year-old woman was killed in Mae Sai district after a wall in her house collapsed.
Terrified residents across the region fled their homes, tall buildings swayed and hospitals and schools were evacuated during the tremors.
In Yangon Chris Herink, Myanmar country director for the charity World Vision, said there did not appear to be "catastrophic infrastructure damage" in the affected areas of Kengtung and Tachileik, although buildings were cracked and water supplies disrupted in some areas.
"Of real concern though are the more rural areas. There will be more, I am afraid to say, unhappy information coming throughout the day," he said.
"It is a hilly area near the border between Thailand and Laos, the so-called Golden Triangle. There is a lot of commerce that goes on in the area." World Vision has around 7,000 children sponsored by overseas donors in the affected areas.