The bus was one of three carrying police near Salta, a city about 1,500 kilometres north of Buenos Aires.
"For reasons that are still unknown, the bus lost control while entering the bridge and fell into the creek bed below," said a statement issued by the National Gendarmerie, a special police force typically charged with patrolling frontier regions.
Local television images showed rescue crews working around the overturned bus, which authorities said was carrying around 60 people.
The group was heading to the province of Jujuy, the country's most northern region that borders Bolivia.
More From This Section
Roads in Argentina, a large country with a land mass about four times the US state of Texas, are poorly maintained in many rural areas.
The government announced that Security Minister Patricia Bullrich and National Gendarmerie director Omar Ariel Kannemann were travelling to the scene.
The crash comes as President Mauricio Macri begins his first full week in office. He issued a statement offering condolences to the families of the victims.