The alleged shooter was taken into custody after an attempted robbery at Roosevelt Field mall about 1 p.m., Nassau County Executive Edward P. Mangano told reporters.
The victim, an unidentified mall employee, was struck in the shoulder outside the store by a stray bullet, Mangano said.
Witnesses described a stampede of shoppers leaving the mall. Some people hid in stores after workers shuttered the gates following the sound of a gunshot and screams.
The alleged shooter had gained access to the Rolex section of a high-end Tourneau watch store, Mangano said. A single gunshot was fired.
The suspect was apprehended by a store security guard, police said.
Parts of the mall were evacuated and others placed on lockdown, though the mall remained opened, officials said.
Garden City schools also were in lockdown for a time, according to CNN affiliate WABC.
"As you know, this is one of the most crowded times of the year," acting Nassau County Police Commissioner Thomas Krumpter said of the mall. "There were a significant number of people near the Tourneau store."
Video from the scene showed shoppers standing outside the mall in small groups, some talking on cell phones. Heavily armed officers descended on the shopping complex.
"Everybody was just running out of the mall," one shopper, Mary Hartill, told CNN affiliate News12.
Jessica Julig told WABC she was shopping when employees suddenly told her to stay down.
She heard screams, Julig told the station, then "started to feel the whole mall shake."
People were running, according to Julig. Mall workers escorted her and others to a service entrance.
Maria Levato said she was separated from her family.
"A bunch of people just started, like, stampeding, so the store manager was very good, and had everyone in the store go down to the basement in ... the back office," she told CNN affiliate WCBS.
"We just waited there for an hour until we heard everything was clear."
A wild rush of people dashing through the food court interrupted Roxanne Steel's lunch break, she told the station.
"There were a gang of people basically trampling me, babies, older people," Steel said.
Gene Robbins and his wife were locked in a store. They learned of the shooting via reports on their smart phones, he said.
"They held us in the store and wouldn't let us go out," Robbins told WCBS.
Police responded to the robbery as a possible active shooter situation.
"That's how we respond in this day and age," Mangano said.