A 12‑year‑old girl has been hospitalised after she was found with a laceration to her face during an alleged domestic violence incident in Sydney’s south‑west.

Emergency services were called to a home on Supply Ave in Lurnea, about 10am on Sunday, where they found the girl injured along with two other people suffering minor wounds.

NSW Ambulance paramedics treated all three at the scene before the girl was taken to Westmead Children’s Hospital in a stable condition.

Officers from Liverpool City Police Area Command established a crime scene and launched an investigation.

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A 20‑year‑old man was arrested a short time later and taken to Liverpool Police Station.

Inquiries are ongoing.