Lynskey was born in New Plymouth, New Zealand, to Kay Lynskey, a real estate agent, and Tim Lynskey, an orthopedic surgeon. Their surname is Irish. Lynskey is the eldest of five children, and has three brothers and one sister. Growing up, she was often solely responsible for the care of her siblings. Lynskey was raised in the Baptist faith.
When she was six, Lynskey's family moved to England for one year before returning to New Zealand. She recalls moving "a lot" due to her father's profession: "My dad was a medical student when I was born, so he was studying and going to different universities. And then he was doing his residency, so I was always the new kid in school". She later attended New Plymouth Girls' High School, where she was involved in the drama department and school plays. She has spoken about being shy at school and finding comfort in acting: "It was so freeing, having someone give me the words to say and not being myself for a minute. It just felt like a weight was lifted off my shoulders". After graduating high school, Lynskey studied for eighteen months at Victoria University of Wellington, majoring in English literature, but dropped out to focus on her film career.