The official Xinhua news agency said in a report late on Sunday three armed groups simultaneously attacked security posts in the border towns of Muse and Kutkai in Myanmar's northeastern Shan state earlier in the day.
Xinhua, citing unidentified sources, said there were military and civilian casualties but gave no other details.
China's defence ministry said in a statement on its website it hoped that calmness and restraint would be exercised to prevent further escalation.
"The Chinese army is on high alert and will take the necessary measures to safeguard the country's sovereignty and safety, as well as protect the lives and property of Chinese
citizens living along the border," the ministry statement said.
Thousands of people have been displaced by decades of fighting between the military and ethnic armed groups in Shan state, which is home to several large groups operating close to the borders with China and Thailand.