Police said the 29-year-old man was attacked at the Gorbals venue's Island Bar at about 01:30.
He was taken to the Queen Elizabeth University Hospital but was released after treatment.
His attacker was white, in his late teens to early 20s, between 5ft 7in and 6ft tall, with short, dark hair. He was wearing a white polo shirt and light-coloured knee-length shorts.
Det Con Lee-Anne Miller, of Police Scotland, said: "The injured man was standing in the bar area when he became involved in an altercation with the suspect which then led to a fight in which he was stabbed.
"Thankfully no-one else was injured but with the number of people about, this could have escalated quite easily.
"We are working with staff from the venue, who quickly stepped in to stop the fight, and we are checking CCTV inside the premises to identify the person responsible for the attack."
She added: "The gig was packed at the time of the assault and a number of people have been spoken to regarding what they saw, however, I am still keen that anyone who witnessed the incident contact police."

"I'm 64," he said of his fascination with the 1836 battle. "When I was five or six years old, this thing began."
Collins' collection includes a fringed leather pouch used by Davy Crockett and Jim Bowie's legendary knife.
"There's things in there that will make your mouth drop," the Genesis star said in San Antonio.
The donation was accepted on Tuesday by Texas Land Commissioner Jerry Patterson, who is campaigning for a new historical centre to house Collins' collection.
"Texans are deeply indebted to Phil Collins,'' Patterson said. "He is giving us back our heritage.
"Now these Texas treasures need a home where all can see them and study from them and learn about how Texans won our liberty.''
The legendary battle, named after a former mission in San Antonio, saw 1,500 Mexican troops lay siege to 200 Texans fighting for Texas independence.
Collins said he first became interested in the Alamo after watching a 1950s TV series about Crockett, the famed frontiersman who died in the conflict.
The Grammy and Academy Award winner's collection includes more than 200 items and is thought to be the largest in private hands.
"My nine-year-old son was saying, 'Why are you going to give it all away, Dad? I thought I was going to have it,''' he told reporters.
A man has been stabbed in a bar at the 02 Academy in Glasgow.
[NEXT_CONCEPT]
Singer Phil Collins has handed over his large collection of Alamo memorabilia to a Texas museum, calling the donation the end of a six-decade "journey".