An eight-year-old boy who was traveling on the top of the bus died at the scene as a result of his injuries, while a woman, believed to be a pedestrian in her 70s, also died at the scene, the police said.
The collision occurred at 6 p.m. local time after the bus collided with a number of stationary cars and a lamppost before crashing into a Sainsbury supermarket, according to the police.
A nine-year-old girl, also on the top of the bus, was seriously injured and was now receiving treatment at Birmingham Children's Hospital. Five other people suffered minor injuries and were receiving hospital treatment.
Police were investigating the cause of the accident and trying to establish the circumstances around the collision. A number of road closures were in place and buses were unable to drive into the city center, West Midlands Police said.
"This is a busy area of Coventry city center and we hope to keep disruption to a minimum as our investigation continues; no-one has been arrested at this stage," said Superintendent Paul Keasey, head of the Central Motorway Police Group.