Cheryl Jennings of New Castle is charged with first-degree murder in the killing of 19-year-old Malcolm Evans.
Police say community tips led them to the accused killer.
Police say Evans, a Delaware State University student, was on his way to work at FedEx on July 9 when Jennings fired a bullet into his car, hitting him in the chest.
Police have not released a motive.
Detectives found Evans' vehicle crashed in the 600 block of Country Path Drive in the Rutledge development, where they both lived.
He died later that day in the hospital.
Terry Evans, Malcolm's mother said, "Over the last six weeks my family and friends have spent so many sleepless nights wondering who and why would commit such an unspeakable crime against such an amazing young man."
She spoke tearfully at New Castle County Police headquarters, after the announcement of an arrest in her son's death.
The announcement comes about a month after police and the Evans family made a public plea for information, and offered a $40,000 reward.
Evans' father, Kevin, says his son's goal was to become a doctor.
Evans was a listed organ donor and saved four people after his death. His kidneys, liver, and heart were all donated.
"He wanted to be a doctor and the way that we look at this is he saved four lives at one time," Kevin Evans said.
A neighbor who doesn't want to be identified says, a few weeks ago, she saw investigators gathering evidence at the house where Jennings lives on Terry Court, not far from the neighborhood entrance.
"I was shocked. I mean, I don't know the lady very well, I've only spoken to her a few times. But I never would've thought this would happen," she said.
On Wednesday authorities were back and, this time, she says a SWAT team surrounded the house with guns drawn.
"All of a sudden, before you know it, a SWAT team was here and then you heard a sound that sounded like a cannon and obviously that was the front door. And then after that, about 10 to 15 minutes, you saw them bring her out.
Police have not released the arrest documents, saying they are sealed because this is an ongoing investigation.