Police said they arrested three suspects in Wednesday’s attack. A police source said Rohingyas, as they are called, threw at least two petrol bombs at the building. Witnesses said this followed an argument with embassy staff.
About a quarter of a million Rohingya refugees have fled Myanmar saying they were persecuted under the military government there.
The building was gutted by the fire and police and fire crews sealed off access to the embassy.
Myanmar officials were not available for comment.
Tens of thousands of immigrants from Myanmar live in Malaysia, which is one of southeast Asia's wealthiest countries and a magnet for migrant workers. Malaysia also attracts hundreds of asylum seekers who claim they face persecution from Myanmar's military rulers.
The fire is the second security breach at a diplomatic mission in Kuala Lumpur in the past eight days, though they appear to be unrelated.
On 30 March, someone threw an explosive device at Australia's High Commission in the city, scorching an outer wall, but causing no major damage or injuries. Police said the device was a bottle filled with firecracker powder. No arrests have been made.