The incident occurred when the driver of the Uttar Pradesh state roadways transport corporation (UPSRTC) bus lost control over the vehicle and it rammed a tree, police said.
Ram Prakash (50) and Netrapal (40) were killed in the accident, they said.
The injured passengers have been shifted to the district hospital, the police said.
In a separate incident in the district yesterday, 14 people were killed and 28 others injured when a truck carrying a marriage party fell into a canal.