The accident occurred shortly before 6am on a secondary road between Endingen and Lengnau, northwest of Zurich, Aargau cantonal police said.
The man and woman who died were bus passengers, while three others on board were hospitalized for injuries after the bus was struck on one side by a truck-trailer, police told local media.
The truck then flipped over and struck a car driving behind the bus, police said in a statement.
The 22-year-old truck driver was slightly injured, while a 29-year-old man and a 28-year-old woman in the car suffered more serious injuries, the statement said.
Emergency workers had to use the jaws of life to pry the pair out of the car, which was a write-off, police said.
Media video footage showed the truck flipped on one side along with its trailer, while the wrecked car ended up in a ditch.
Pictures showed the 355 Swiss Post bus sustained damage on one side but remained upright.
Carrying seven passengers, it was travelling toward Niederweningen.
The driver of the bus escaped injury, police said.
The road was closed for several hours while emergency services responded to the accident scene.
Officials have launched an investigation into the cause of the accident.
Photo: SRF/Beat Kälin