The U.S. Geological Survey (USGS) said the quake struck near the town of Chauk, on the Ayeyarwaddy River south of Bagan and about 175 km (110 miles) southwest of the country's second city Mandalay, just after 5 p.m. (1030 GMT).
Fire department and Red Cross officials said two children were killed in the small town of Yenanchaung, south of Chauk.
"Two young girls died when a pagoda collapsed on a river bank," said Moe Thidar Win, deputy director of the disaster management team at the Myanmar Red Cross Society.
"One man died in a Pakokku tobacco factory when the roof collapsed on him."
In Bagan, known as the "City of 4 Million Pagodas", one female tourist was injured at a pagoda, said local official Khin Mya Lwin.
The Ministry of Information said nearly 100 of Bagan's famed pagodas, mostly built between the 11th and 13th centuries, had been damaged.
Bagan has around 2,000-3,000 pagodas and temples, spread over a 42-sq km plain ringed by mist-covered mountains. It rivals Cambodia's Angkor Wat and Borobudur in Indonesia as Asia's premier archaeological site.