SINGAPORE—Myanmar authorities declared martial law in parts of Yangon after scores were killed and fires tore through several Chinese-owned garment factories, underscoring the threat to the nation’s fragile economy and tensions over China’s role in the country.

At least 37 people were killed on Sunday as authorities opened fire to disperse protests in two industrial suburbs of Yangon, Myanmar’s largest city, emergency responders said. At least 15 others were killed elsewhere, according to the Assistance Association for Political Prisoners, a nonprofit that monitors arrests and fatalities.

Sunday’s violence capped the deadliest weekend since Myanmar’s military seized power on Feb. 1, detaining civilian leaders, including Aung San Suu Kyi, and abruptly ending the country’s decadelong transition to democracy. The factories burned in the Yangon suburbs of Hlaing Tharyar and Shwe Pyithar, rattling one of the country’s most important export industries and drawing a rebuke from China.

The Chinese Embassy in Yangon condemned the attacks as “especially vile” and urged Myanmar authorities to stop the violence, punish perpetrators and protect Chinese businesses and personnel in the country. The embassy said multiple Chinese-backed factories were smashed up and set alight, while many Chinese nationals were injured. Most of the affected businesses were textile and clothing factories, it said.