Charges are pending against the teen, whose identity is not expected to be released because of his age.
The victim, Samuel Poulin, was not the intended target.
The shooting happened the evening of Sunday, June 27, near 1535 Broadway, at Seventh Avenue and 46th Street, where authorities say a group of five or six CD vendors was arguing under the Marriott Marquis sign.
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One pulled out a gun and fired a shot, and Poulin -- with his family just a few feet west under the Starbucks sign -- was grazed in the back.
The bullet was visible and did not pierce through his body, and he suffered non-life-threatening injuries and was taken to Bellevue Hospital.
"The Citadel family - in Charleston, South Carolina and around the world - is greatly saddened to learn about what happened to our Class of 2021 graduate, 2nd Lieutenant Samuel Poulin in Times Square on Sunday when he was hit by a bullet from a shooting event unrelated to him," Citadel President Gen. Glenn M. Walters said in a statement. "We are encouraged that he is reported to be in stable condition are sending our prayers and our love to his new wife and his family. 2nd Lieutenant Poulin holds a Bachelor's Degree in Physics, was a President's List cadet and exemplifies the kind of principled leader The Citadel strives to produce."
No one else was injured in the shooting.
As a result of the incident and a general spike in crime, Mayor Bill de Blasio said 50 more NYPD officers would be assigned to Times Square.
"It is just an unacceptable state of affairs," he said. "This is a place that is precious and so important to New York City. It has to be safe, so we are adding additional officers."
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He added that they would be stepping up enforcement against illegal vendors as he and NYPD Chief of Detectives Rodney Harrison announced the "Times Square Safety Action Plan."
"The bottom line is we are going to flood the zone in Times Square with additional officers to make sure this situation is resolved once and for all," de Blasio said.
Back in May, a shooting in this same area of Times Square wounded two women and a 4-year-old girl.
A suspect was later arrested in Florida.
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