It could be felt in the north-east Indian state of Assam, where the Duke and Duchess of Cambridge are staying.
The royal couple, who are staying in a national park, were unharmed.
Tremors are relatively common in Myanmar (formerly known as Burma).
An Associated Press news agency reporter in the city of Yangon reported seeing a seven-storey hospital shake during Wednesday`s two-minute quake, causing staff and patients to flee the building.
Many of Myanmar`s outlying areas have inadequate communications and infrastructure, including the area where the earthquake hit.
The Chinese official Xinhua news agency said strong tremors had also been felt in Tibet, with many residents of Lhasa drawn out on the streets.
The quake was also felt in the Bangladeshi capital of Dhaka, 484km (300 miles) from the epicentre and in the Indian city of Kolkata.
Similar shaking was experienced in the Assam capital Guwahati, where wall-mounted television sets at a local TV station were reported to have been sent crashing to the ground.
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