The quake struck 25km (15.5 miles) west of Chauk, at a depth of 84km, the US Geological Survey said.
Tremors were felt as far away as Thailand, Bangladesh and India, sending fearful residents into the streets.
At least 66 stupas in Bagan have been damaged, a spokesman from the department of archaeology told the BBC.
A 22-year-old man was killed in the town of Pakokku due to a building collapse.
Videos posted on social media from Bagan show clouds of dust and the tops of some pagodas crumbling as the quake struck.
The ancient capital is a major tourist site, home to thousands of Buddhist monuments.
Earthquakes occur regularly in central Myanmar and the temples have been damaged and reconstructed before, the BBC's Myanmar correspondent Jonah Fisher says.
There are numerous reports of buildings being damaged elsewhere in the country, including the parliament building in Naypyidaw.
Tall buildings shook in Yangon, Myanmar's largest city, the Thai capital Bangkok and Kolkata in India, where underground railway services were temporarily suspended.
At least 20 people were injured in the Bangladeshi capital, Dhaka, as they fled a building, local media report.
A 6.8 magnitude earthquake has hit central Myanmar, damaging pagodas in the ancient city of Bagan and killing at least one person.