Artillery and small arms fire were used in the town of Laukkai, in the Kokang region.
Fighting reportedly erupted after rebels dressed in police uniforms launched a surprise raid.
Five civilians, five police officers and at least 20 rebel fighters are said to have died.
The office of Myanmar's de facto leader, Aung San Suu Kyi, said in a statement: "According to initial information, many innocent civilians including a primary school teacher... were killed because of attacks by the MNDAA armed group."
The Myanmar Nationalities Democratic Alliance Army (MNDAA) is a rebel group fighting Myanmar's armed forces in the region.
Officials said the attack was launched early on Monday, and targeted police and military posts. A separate group of fighters later attacked other sites in Laukkai.
Video shared on social media appeared to show parts of the town on fire on Monday afternoon, as civilians ran to safety.
An army source told the AFP news agency that the fighting was ongoing as darkness fell.
"Residents in town are fleeing. We do not know exact figures yet," the officer said.
What is Myanmar like?
The Northern Alliance, a multi-faction rebel group which includes the MNDAA, confirmed on Facebook that its members were fighting in Laukkai.
It said the attack was carried out in "self-defence", citing operations by the Myanmar military since December.
The violence is among the worst to hit the Kokang region, in the northern part of Shan state, since 2015.
The worsening conflict in the borderlands has raised tensions between Myanmar and much larger China.
Kokang has close ties to China, with locals speaking a Chinese dialect and using the yuan as currency.
Ms Suu Kyi's government is desperate to end the decades-long violence, amid fears it could spark a new refugee exodus.
At least 30 people have been killed on Myanmar's border with China, after clashes between ethnic rebels and the security forces.