Authorities said bystanders jumped on the car and banged on its windows as it ploughed through crowds of pedestrians.
Clark County Sheriff Joe Lombardo told reporters that 24-year-old Lakeisha N Holloway would not stop and it appeared from video that it was an intentional act.
Her three-year-old daughter was in the car but was not injured.
He said that after the incident, Holloway drove to a hotel and told a valet to call 911 after explaining what she had done.
Mr Lombardo said police believe she had had an argument with the father of the child before the crash.
A drug recognition expert on the scene determined Holloway was under the influence of a “stimulant”, but blood test results are pending.
Mr Lombardo said Holloway is believed to be from Oregon and had been in Las Vegas for about a week. He said investigators believe she was living in the car.
The crash occurred on a busy stretch of the Strip in front of the Paris and Planet Hollywood hotels, across from the dancing water fountains at the Bellagio, where visitors crowd pavements as they walk from one casino to another.
The Miss Universe pageant was being held at the Planet Hollywood resort at the time.
Jessica Valenzuela, 32, of Arizona, died in the crash.
The vehicle was in the northbound lanes of Las Vegas Boulevard near Bellagio Way when it drove up on to the pavement in front of the Paris hotel and struck pedestrians.
After the crash, the vehicle continued to head east on Flamingo Road before it was found at a hotel.
Prosecutors said they expect to file murder charges and other counts against the driver.
Clark County district attorney Steve Wolfson said the vehicle could be considered a deadly weapon, adding: “When a person drives a 2,000lb-plus motor vehicle intentionally on to a sidewalk, killing and injuring scores of people, that’s murder.”