Odjig was born in 1919 at Wiikwemkoong, the principal village on the Manitoulin Island Unceded Indian Reserve, to parents Dominic and Joyce (née Peachey) Odjig. She was the eldest of four children; her siblings are Stanley, Winnifred and Donavan. She was descended on her father's side from the great Potawatomi Chief Black Partridge.  Her mother, an Englishwoman, met and married Dominic in England where he was serving during World War I.

When Odjig was 13 years old, she suffered rheumatic fever and had to leave school. Recuperating at home, she spent time with her paternal grandfather, Jonas Odjig (a stonecarver), and her parents - all of whom encouraged her to explore art. Odjig later said that her grandfather "played a great role in my life – he nurtured my creative spirit – he was the first one I ever drew with ... he was my first mentor." Odjig was also influenced by her mother, who embroidered, and her father, who liked to draw war scenes and his officers from his wartime experiences. Odjig once stated that "Art was always a part of our lives".

When she was 18, Odjig's mother and grandfather died. Odjig moved to Parry Sound, Ontario, and then at the outbreak of World War II, she moved to Toronto for job opportunities. She worked in factories and in her spare time explored art galleries such as the Royal Ontario Museum and the Art Gallery of Ontario. She was particularly influenced by her first experiences of cubist art by artists such as Picasso.