Jones, 35, of Kernersville, North Carolina, turned himself in to police on Thursday, accompanied by a lawyer.
Szabo later died as a result of his injuries at a NY hospital.
When the man allegedly banged on Jones' auto, the second-year Wake Forest coach reportedly punched him.
After he punched Szabo, police say Jones got into an SUV and drove away leaving the man on the pavement.
Wake Forest released a statement Thursday night saying, "We have just been made aware of this matter and we are gathering information".More news: Pence outlines plan to create U.S. Space Force by 2020
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Szabo, visiting from Boca Raton, Florida, banged on the window of Jones' SUV while looking for his ride after his stepsister's wedding, police said. Jones was released on his own recognizance and was ordered to return to court on October 2.
"It's an unfortunate and tragic incident", Jones' attorney, Alain Massena, told ESPN.
A spokesman said Wake Forest had no immediate comment on the 35-year-old Jones' arrest.
Jones is set to begin his second season on Danny Manning's Wake Forest staff after joining in the spring of 2017. The Jones family sends their deepest condolences and sympathies to the Szabo family.
Prior to coming to Wake Forest, Jones coached at Central Florida, VCU and Florida Gulf Coast. "Sandor was super outgoing, friendly, and an incredibly smart businessman", his company, What If Media, said in a Facebook post Wednesday.
"His attractive spirit and his love of life will remain with us", the company said.