The victim has been identified as Dharmendra Kumar and was part of a team of the education department from Varanasi that had brought Uttar Pradesh Board high school examination answer sheets to a college in Muzaffarnagar, Superintendent of Police (City) Satyanarain Parjapat said.
The head constable, Chander Prakash, was part of the police team that accompanied Kumar and a few other officials from Varanasi.
Mr Parjapat said that Kumar had a confrontation with Prakash while they were in the vehicle on Sunday night.
"The constable was under the influence of alcohol and was constantly demanding tobacco from the teacher. However, when the teacher did not give tobacco, an argument broke out between them and the policeman opened fire at him using his service weapon," Mr Parjapat said.
The school officials and the police team had left Varanasi on March 14 and had submitted the answer sheets at colleges in other districts.
After submitting the copies in Prayagraj, Shahjahanpur, Pilibhit, Moradabad and Bijnor, they reached the SD Inter College in the Civil Line area of Muzaffarnagar on Sunday night. They were then waiting in the vehicle for the college gate to open when the incident took place.
The injured teacher was rushed to a hospital where he was declared dead, Mr Parjapat said.
Police have sent the body for post-mortem and have registered a case against the head constable. They are also questioning all others present in the vehicle.