Such accidents are a regular occurrence in the former French colony, where the poor state of the roads has been a source of social tension.
Transport Minister Dembele Madina Sissoko said the dead included a baby after the passenger bus collided with a lorry carrying agricultural produce near the town of Segou.
He stressed it was a provisional toll, and blamed bad weather.
Three of the injured were seriously hurt, Sissoko added.
The government had at first stated on social media that 37 people were killed in the accident at Zambougou, without detailing the circumstances.
Alassane Traore, governor of the Segou region which includes Zambougou, told AFP the crash “is the consequence of driving in the rain.”
A crash survivor said “visibility was poor and the road was wet because of the heavy rain,” adding the truck failed to brake in time.
The transport minister told AFP the government will investigate the incident.
“May Allah welcome the souls of the deceased to paradise,” he said.
Travelling by road is still the principal means of transport for people and goods in the landlocked Sahel nation of some 20 million people.
In neighbouring Senegal, 11 people were also killed in a road accident in the north of the country on Tuesday morning, the government said.