Police described the suspect as being a local Las Vegas man who acted alone, Sheriff Joseph Lombardo of the Las Vegas Metropolitan Police Department said at a briefing. But authorities were seeking an Asian female who police described as a companion of the suspect, he said.
They said that rumours of other shootings in the area were false. Off-duty police were believe to be among the victims.
Witnesses on social media said the shooting broke out on the last night of the three-day Route 91 Harvest festival, a sold-out event attended by thousands and featuring top acts such as Eric Church, Sam Hunt and Jason Aldean.
The spokeswoman for the University Medical Center hospital said 14 of the wounded were in a critical condition. All had suffered gunshot wounds, she said.

The shooting broke out on the last day of the Route 91 Harvest Festival
"Confirming that one suspect is down. This is an active investigation. Again, please do not head down to the Strip at this time," Las Vegas Metropolitan Police Department said on Twitter.
The gunman, who was a local man, was killed after police "engaged the suspect," Las Vegas Sheriff Joseph Lombardo told reporters.
Police said on Twitter that at this time they did not believe there are any more shooters.
Las Vegas is an internationally renowned major resort city, known primarily for its gambling, shopping and entertainment.
Video on the festival's website showed stage set up outside the front of the Mandalay Bay.

Fourteen victims who were in critical condition had all suffered from gunshot wounds
One Twitter user posted that the casino hotel was on lockdown, while another, citing police scanners, said two gunmen who had shot at a bodyguard and police were on the 32nd floor, although there was no confirmation from police.

The Mandalay Bay Hotel Casino is allegedly on lockdown.
Witnesses heard numerous gunshots at the hotel, where police tactical teams were searching for the attacker, according to reports on CNN and in the New York Times.
Police have disclosed no information that would suggest a motive for the shooting or revealed the identify of the suspect.
Even so, the rampage was reminiscent of a mass shooting at a Paris rock concert in November 2015 that killed 89 people, part of a coordinated attack by Islamist militants that left 130 dead.
(Editing by Chris Michaud and Frank McGurty in New York; writing by Alison Williams; Editing by John Stonestreet)
© Thomson Reuters 2017
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)