The star, born Abel Tesfaye in Canada, is the son of Ethiopian immigrants.
"My heart breaks for my people of Ethiopia as innocent civilians ranging from small children to the elderly are being senselessly murdered," he said.
Fighting between the Ethiopian army and the Tigray People's Liberation Front (TPLF) began in November and has left millions of people homeless.
The fighting started when Prime Minister Abiy Ahmed sent forces to the Tigray region, after accusing the TPLF of attacking a government military base.
The TPLF had been the ruling party in the area, but fell out with Mr Abiy over his efforts to increase the central government's power.
Last week, a BBC Africa Eye investigation uncovered evidence suggesting the Ethiopian military had carried out a massacre in Tigray, killing at least 15 men.
So far more than two million people have left their homes to get away from the fighting, according to Tigray's interim administration.
It has left more than four million people in need of aid, they added.
The Weeknd said on Twitter and Instagram that his $1m donation would go to the UN's World Food Programme to pay for two million meals.
The singer has become one of the biggest chart stars of the last decade with hits including Blinding Lights.
He has spoken before about his Ethiopian heritage, telling Rolling Stone magazine in 2015 that his grandmother would take him to services at their Ethiopian Orthodox church in Canada, that his first language was Amharic, and that his vocal style was influenced by Ethiopian singer Aster Aweke.