The accident occurred 80 km (50 miles) south of Harare when the bus tried to overtake a vehicle, but rammed into an oncoming lorry and overturned three times.
In March, Prime Minister Morgan Tsvangirai was injured and his wife killed in an accident on the same Harare-Masvingo highway, one of the many roads neglected during the country’s economic collapse.
Police spokesman Andrew Phiri said 33 people died on the spot, while four others died later.
Twenty-nine people were injured in the accident.
Phiri said the accident occurred when the bus driver tried to overtake a vehicle.
One person from the truck was also killed.
He, however, did not mention who many people were on board the vehicles at the time of the accident.