The 6.8-magnitude quake struck some 120km (70 miles) north of the second-largest city of Mandalay, at a depth of 10km, the US Geological Survey said.
A bridge under construction collapsed in Shwebo, close to the epicentre, throwing workers into the river.
In the early hours of Monday a second quake, of 5.6 magnitude, struck the same region, the USGS said.
There was no immediate information on whether the latest quake caused further deaths or major damage.
The first earthquake hit at 07:42 local time (01:12 GMT), the US Geological Survey said.
In Mandalay, terrified residents dashed out of their homes for safety, fearing more tremors.
An official in Sintku township near the first quake's epicentre told Associated Press six people had died there, some of them workers at a gold mine that collapsed. A number of people were injured.
A police officer in Shwebo said five construction workers who had been working on the Radana Thinga bridge near the town were missing after "a huge steel beam fell into the river".
He told Reuters that one woman had also died and 10 people had been injured in the nearby town of Kyauk Myaung after a house collapsed.
Temples were reported damaged at Mogok, close to the epicentre.
An official from Burma's Relief and Resettlement Department told Agence France-Presse the death toll could rise.
"This is the worst earthquake I felt in my entire life," 52-year-old Shwebo resident Soe Soe told Associated Press.
Save The Children told AFP it had reports of 13 deaths across four sites in Burma, with some 40 people injured.
Residents in Mandalay described panic in the streets as they fled the shaking buildings.
"I ran from my bed carrying my daughter out to the street. There were many people in the road. Some were shouting and others felt dizzy," San Yu Kyaw said.
"People are now scared of more earthquakes," he added.
The earthquake was felt as far away as Bangkok in neighbouring Thailand.
The US Geological Survey issued a yellow alert, indicating that "some casualties and damage are possible".
Earthquakes are relatively common in Burma.
In March 2011, at least 75 people died when a powerful earthquake hit Burma near the borders with Laos and Thailand.
A strong earthquake has rocked central Burma, with at least 12 people feared dead and dozens more injured.