Images of the incident showed the completely mangled front end of a white bus, with blood-flecked seats, personal items and a shoe strewn around the tree-lined crash site.
"In view of this tragedy, the head of state extends his deepest condolences to the families of the victims and wishes a speedy recovery to the injured," the government statement said.
Public prosecutor, Cheikh Dieng, said in a statement that early investigations suggested a public passenger bus suffered a burst tire and swerved off course.
It then crashed "head-on with another bus coming in the opposite direction", he said.
Colonel Cheikh Fall, who heads operations for the National Fire Brigade, told AFP the victims were taken to a hospital and medical center in Kaffrine.
The crash, one of the deadliest in the West African country's recent memory, was on one of the main east-west arteries near the town of Kaffrine, about 220 kilometers southeast of the capital, Dakar.
President Macky Sall said on Twitter that he was "profoundly saddened" by the accident and announced three days of mourning starting on Monday.
In a tweet, President Sall said that after the period of national mourning finished, a government council will be held to "take firm measures on road safety."
Road accidents are common in Senegal, where large trucks and buses, often decades old, overburdened and listing, hurtle down two-lane highways pitted and rutted by overuse.