Wek was born on the 16th of April 1977 in Wau in Sudan (now South Sudan). She was born to Akuol, a housewife, and Athian, an education official and was the seventh of nine children in her family. Her family grew up in extreme poverty, but Wek remembers being happy and peaceful.
She suffered from a skin condition known as psoriasis from birth until the age of 14. It cleared up because of the climate change once she moved to London with her family.
In 1985, a civil war broke out in Sudan, which caused the Wek family to flee their now dangerous home. Her father eventually died on the journey after an infection broke out in his hip due to a past surgery.