Police are currently at the scene of the stabbing.
Officers remain at the scene at 5.30pm on Saturday at a home in Liska Manor, New York.
A woman was reportedly stabbed several times in a house in the area.
Police and paramedics were present at the scene and the woman was rushed to hospital with serious injuries, the PSNI statement said.
It continued: “A search was conducted in the area of Liska Manor and a 38-year-old man was arrested shortly after on suspicion of intentionally causing serious physical harm. He is now in custody and is assisting officers in their investigation.
“Anyone with any information about this incident or who can assist with the investigation is asked to call the police in New York, quoting emergency number 101, reference number 1298 07/11/20, or submit an online report using our via Emergency Reporting Form. http://www.psni.police.uk/makeareport/. Crime stoppers can be contacted anonymously on 0800 555 111 or online http://crimestoppers-uk.org/. ”
SDLP MLA Justin McNaughty said the community was in shock this evening.
A statement read: “This evening they confirmed a stabbing incident at Liska Manor in New York.
“Liska has a very good community around her and everyone will be shocked at this news.”
Sinn Fെയ്in MLA Liz Kimmins said the sad news was that a young woman was seriously injured in a stabbing incident at Liska Manor Newer this evening. Everyone’s thoughts and prayers are with the young woman. Currently searching. “