Amanda Malloy, 29, of Melville, was killed in the 7:25 p.m. accident on New York Avenue, police said.
The driver, Shea Rosen, 19, of Wheatley Road, Brookville, was arrested and charged with misdemeanor driving while ability impaired by drugs, police said.
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Those charges likely will be upgraded, the prosecutor said.
Rosen pleaded not guilty at his arraignment at First District Court in Central Islip, where he was ordered held on $500,000 bail, or $1 million bond.
Rosen was driving home from nearby Prime Restaurant, 117 New York Ave., when he came upon the joggers, authorities said.
"I didn't see her," the driver told police, according to the prosecutor, Avemaria Thompson. "She was running in the road."
Police reported the driver to be unsteady, with glassy eyes and a smell of marijuana on his breath, according to the prosecutor.
Thompson said that, when asked to take a breath analyzer test, Rosen told police: "I'm not taking anything. No way. I'm not taking that."
Three pills were found in the driver's sock, the prosecutor said.
More than 12 hours after the fatal accident, Rosen's brown 2000 Dodge Durango sport utility vehicle remained stopped in the southbound lane of New York Avenue not far from Madison Street and Heckscher Park.
A running shoe lay in the street near the open rear hatch. The hood was dented.
The scene remained cordoned off with yellow police tape Friday morning.
A passerby said Malloy was a fourth-grade teacher at John F. Kennedy Elementary School in Deer Park, where his son is in her class.
"She's a very avid biker. She rides her bicycle to school," Tony Etersqua said.
Malloy also ran marathons and had a black belt in karate, he said.
"She's a very well-spoken person, well liked," Etersqua said.
The school held parent-teacher conferences last week and Etersqua said Malloy had a positive and generous spirit.
"She was looked upon as a teacher who did good. She always had a smile on her face," he said. "This girl had her whole life ahead of her."
The school has grief counselors on hand this morning, Etersqua said.
"We were really blessed to have her as our son's teacher," he said.