Kershaw was born in Melbourne. She is the daughter of Kerry, a Psychologist, and Kim Kershaw, who played in the Victorian Football League for Richmond and Hawthorn. She has said that as a child, she was "always in the hospital." At age four, she suffered from meningitis and had to have two spinal taps. She also had a tumour on the knee, and several broken bones from climbing trees. She grew up in Kensington and attended St Michael's Catholic Primary school in North Melbourne. She has stated that she "grew up with 42 nationalities", explaining that her primary school of 150 children was very multicultural. She then attended the Academy of Mary Immaculate in Fitzroy. She later went on to win the Australian 2004 Girlfriend Model Search. She once worked at McDonald's. After high school, in 2005, she moved from Melbourne to Sydney to begin modelling. She lived 100 metres from the beach and it was while at the beach where she was scouted by Chic Management's Kathy Ward, the model scout that also discovered Miranda Kerr and Samantha Harris. She signed with Chic Management within weeks.

In 2007, Kershaw signed with Next Management and by March had moved to New York City. On 11 December, Models.com named her the "Next Superstar".

Kershaw has starred in the fragrance ads for Gucci's new "Flora" scent since 2008.

In 2010, Kershaw was heavily in demand for campaigns, shoots and shows. Kershaw was featured in the 2010 Pirelli Calendar photographed by Terry Richardson, and the 2011 edition photographed by Karl Lagerfeld. In March 2010, she was announced as the face of Chanel's Autumn/Winter 2010/2011 ready-to-wear ad campaign. This news came after she closed the Chanel Spring 2010 couture show, and opened the Chanel Autumn/Winter 2010/2011 ready-to-wear show. In November, for the fourth time, she became the cover model of Australian Vogue (her previous covers of the same publication were in March 2010, March 2009, and September 2008). The same year, Kershaw was also featured as the face of the Anna Sui FW 2010 campaign.

Kershaw was on the May 2011 cover of Numero, photographed by Tom Munro.

Kershaw has been absent from the runway since the Fall 2012 shows where she walked only for Alexander Wang and Anna Sui. During 2012, she focused on acting and spent much of the year in Africa filming the post-apocalyptic film Mad Max: Fury Road (2015).

Kershaw appeared in the Fall/Winter 2013–14 Campaign for Gucci alongside male model Adrien Sahores, shot by Mert Alas and Marcus Piggott.

In May 2014, Kershaw once again appeared on the cover of Vogue Australia and starred in two editorials on the same issue, in which was celebrate her debut into acting career. In August 2014 Models.com moved Abbey to the Industry Icon list considering her still going presence in fashion with big fragrances contracts as Flora By Gucci and Versace's Yellow Diamond, although she was absent from runways and editorials to film Mad Max and Gods of Egypt.

Kershaw co-starred in the 2015 film Mad Max: Fury Road, alongside Tom Hardy. In 2016, she had major roles the films Gods of Egypt, alongside Gerard Butler, and, as Sarah, in the Nicolas Winding Refn-directed thriller The Neon Demon, with Elle Fanning. In 2017, Lee played Tirana in the film The Dark Tower.