The Indian student, who has not been named, was taken to hospital but was pronounced dead early today morning.
The Greater Manchester Police said the victim was aged 23, and was studying at Lancaster University. His parents in India have been informed of the incident.
"This appears to be an unprovoked attack and we can't establish a motive at this time. We are investigating every possible aspect and we are in the early stages of the investigation but we are not ruling anything out," Chief Superintendent Kevin Mulligan, divisional commander for Salford, was quoted as saying in reports.
The victim was part of a group of nine male and female students, all Indian, who were staying in a nearby hotel for a break in Manchester over the Christmas holidays.
They were heading towards the city centre when they were approached by two white men who were on foot.
The killer approached, engaged the victim in a "very short" conversation, and about a minute later pulled out a handgun and shot the student in the side of the head.
The victim collapsed to the ground as his killer ran away, the police said.
The gunman was described as white, in his mid-20s, of slim build and wearing a grey top. The other man was of a heavier build and wearing a black jacket.
"We can confirm that the man killed in Salford early this morning is a 23-year old Indian post graduate student, who was studying microelectronics," a Lancaster University spokesman said.
"Our thoughts are with his family at this time, and counselling and support has been organised for his fellow students who are deeply upset," he said.
Mulligan sought the help of the local community to track down the killer.
"I believe the answers to who did this will lie in our community. Someone will know who was responsible and I want to implore those people to be courageous," he said.
He said the young man "was simply visiting Manchester with his friends and has been killed, and his family deserve to see those responsible brought to justice".