Twenty-year-old Idrees Merritt is being held without bail, charged with first-degree murder and weapons offenses.
Police say Merritt shot 21-year-old Miprecious Hoskins of Wilmington multiple times.
Her body was found in a trash bin at 3:24 p.m. Wednesday in the 800 block of East 22nd Street, just steps away from a charter school.
The arrest came after investigators spent Thursday scouring Merritt's home on the 2100 block of Locust Street looking for evidence.
Detectives pulled what looked like gloves out of a trash can in back. It was bagged up as evidence.
Hoskin's mother was still trying to process the loss of her daughter.
"I'm still in shock. It's still unbelievable. I'm devastated," said the victim's mother, Mary Dunham.
Dunham said her daughter recently broke up with her boyfriend.
"He was a troubled kid. He had been in and out of jail. He just got out of jail for pulling a gun on both my daughters," said Dunham.
On Thursday afternoon, Sandra Anderson and her goddaughter arrived at the crime scene as investigators searched for clues.
They placed some candles where the 21-year-old's body was found.
"Our hearts in Wilmington, Delaware, are broken," said Sandra Anderson, family friend.