The remains of 24-year-old Valerie Reyes, of New Rochelle, were found last Tuesday in a wooded area on the side of the road in Greenwich.
Police say she was bound at the hands and feet.
The suspect, 24-year-old Javier DeSilva, is currently charged with kidnapping resulting in death. He was arrested at his home in Flushing, Queens, Monday night.
Sources say DeSilva has made admissions in the death, including that it occurred in New Rochelle. Authorities believe he then bound the victim with duct tape, put her in the suitcase and drove her body to Connecticut.
The victim's mother recently said that her daughter was frightened.
"She was just really scared, very frightened," mom Norma Sanchez said. "Fearing for her life."
She says Reyes suffered from anxiety and depression, and that after an ex-boyfriend moved out of her apartment, she became more fearful of dying.
"They released his name, my heart dropped," Sanchez said after learning about his arrest. "It's like, emotions of so much anger and hate, but relieved."
Sanchez said DeSilvia appeared "courteous" and "nice" when they first met, but his disposition seemed to change after the breakup.
"My daughter, she seemed happy," she said. "She wasn't in love, but she loved him in a way...they lasted for maybe like eight months...and then, of course, he became, you know, possessive or not taking no for an answer."
DeSilva is accused of fraudulently using Reyes' ATM card, and police say they believe he was also involved in her death.
"I know a lot of people are going to be relieved, knowing that this monster, that they caught him already," she said. "When somebody, a monster, comes and takes your daughter away or your child away, for what? For what? It's not only hurt. It's hate."