Venko Filipce, the newly renamed European nation's health minister, said seven people were pronounced dead at the scene and the rest died after being taken to a hospital. Six of those injured had life-threatening conditions.
Prime Minister Zoran Zaev declared two days of national mourning.
The bus was carrying about 50 people when it veered off a highway linking Skopje with the western town of Tetovo and plunged 10 meters (30 feet) into a small ravine, landing upside down. The cause of the crash, about 25 kilometers (15 miles) west of Skopje, wasn't yet known.
Firefighters and residents of a nearby village rushed to the scene of the crash to help pull survivors, including the driver, from the wreckage.
Witness Samet Musliu told private Telma TV that rescuers had to cut open the bus to reach the injured.
"There was a strong smell of gasoline and we were afraid the bus would explode," he said.
The bus had been carrying workers back from Skopje to the town of Gostivar, about 80 kilometers (50 miles) southwest of the capital, where most of them lived, said Gostivar Mayor Arben Taravari.